compact mass meaning

(in powder metallurgy) an object to be sintered formed of metallic or of metallic and nonmetallic powders compressed in a die. denoting a tabloid-sized version of a newspaper that has traditionally been published in broadsheet form, (of a relation) having the property that for any pair of elements such that, to pack or join closely together; compress; condense, sediment compacted of three types of clay, to compress (a metal powder) to form a stable product suitable for sintering, a small flat case containing a mirror, face powder, etc, designed to be carried in a woman's handbag, a mass of metal prepared for sintering by cold-pressing a metal powder, a tabloid-sized version of a newspaper that has traditionally been publis hed in broadsheet form, Colorado joins 15 states in favor of popular vote in presidential elections. Fruit should be firm and excellent in condition. The idea of regarding functions as themselves points of a generalized space dates back to the investigations of Giulio Ascoli and Cesare Arzelà. The Dictionary.com Word Of The Year For 2020 Is …. That is, if By the same construction, every locally compact Hausdorff space X is an open dense subspace of a compact Hausdorff space having at most one point more than X. An open covering of a space (or set) is a collection of open sets that covers the space; i.e., each point of the space is Conversely, density is the degree of compactness. "The Definitive Glossary of Higher Mathematical Jargon — Compact", "sequentially compact topological space in nLab", Closed subsets of a compact set are compact, Compactness is preserved under a continuous map, Annales Scientifiques de l'École Normale Supérieure, "Sur quelques points du calcul fonctionnel", Rendiconti del Circolo Matematico di Palermo, Creative Commons Attribution/Share-Alike License, https://en.wikipedia.org/w/index.php?title=Compact_space&oldid=997200956, Short description is different from Wikidata, Wikipedia articles incorporating text from PlanetMath, Creative Commons Attribution-ShareAlike License. a thick, bare trunk crowned by a compact mass of dark-green leaves. It is also crucial that the interval be bounded, since in the interval [0,∞), one could choose the sequence of points 0, 1, 2, 3, ..., of which no sub-sequence ultimately gets arbitrarily close to any given real number. Originally developed in 2000, by … The meaning of "compact" here is not related to the topological notion of compact space. As a Euclidean space is a metric space, the conditions in the next subsection also apply to all of its subsets. Following the initial introduction of the concept, various equivalent notions of compactness, including sequential compactness and limit point compactness, were developed in general metric spaces. The term compact set is sometimes used as a synonym for compact space, but often refers to a compact subspace of a topological space as well. C Compact means to pack or press firmly together. Compactness is a "topological" property. Freeman stands at 6 feet, 5 inches, but he’s always had a compact, whip-like swing. English Collins Dictionary - English synonyms & Thesaurus. ⊂ [4] In general topological spaces, however, different notions of compactness are not necessarily equivalent. to join or pack closely together; consolidate; condense. The following are common elements of massing. ) Towards the beginning of the twentieth century, results similar to that of Arzelà and Ascoli began to accumulate in the area of integral equations, as investigated by David Hilbert and Erhard Schmidt. In mathematics, more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (i.e., containing all its limit points) and bounded (i.e., having all its points lie within some fixed distance of each other). Of all of the equivalent conditions, it is in practice easiest to verify that a subset is closed and bounded, for example, for a closed interval or closed n-ball. Alexandrov & Urysohn (1929) showed that the earlier version of compactness due to Fréchet, now called (relative) sequential compactness, under appropriate conditions followed from the version of compactness that was formulated in terms of the existence of finite subcovers. This is often the starting point of architectural design as it is the big-picture view of the structure of a building. This sentiment was expressed by Lebesgue (1904), who also exploited it in the development of the integral now bearing his name. We would also like a characterization of compact sets based entirely on open sets. This ultimately led to the notion of a compact operator as an offshoot of the general notion of a compact space. Dictionary.com Unabridged In entomology, specifically, compacted or pressed close, as a jointed organ, or any part of it, when the joints are very closely united, forming a continuous mass: as, a compact antennal club; compact palpi. An overview of massing in architecture. If one chooses an infinite number of distinct points in the unit interval, then there must be some accumulation point in that interval. For instance, some of the numbers in the sequence 1/2, 4/5, 1/3, 5/6, 1/4, 6/7, … accumulate to 0 (while others accumulate to 1). Massing is the three dimensional form of a building. These are compact, over-ear headsets that rest comfortably, and that comfort is helped by the lightweight materials used in their construction. US Federal Government Executed 13 Inmates under Trump Administration 1/18/2021 - On Jan. 16, 2021, the federal government executed Dustin Higgs, the thirteenth and final prisoner executed under the Trump administration, which carried out the first federal executions since 2003. an automobile that is smaller than an intermediate but larger than a. For instance, the odd-numbered terms of the sequence 1, 1/2, 1/3, 3/4, 1/5, 5/6, 1/7, 7/8, ... get arbitrarily close to 0, while the even-numbered ones get arbitrarily close to 1. designed to be small in size and economical in operation. ; contract: the proposed economic compact between Germany and France. compact meaning: 1. consisting of parts that are positioned together closely or in a tidy way, using very little…. The Great Russians occupy in one compact mass the space enclosed by a line drawn from the White Sea to Lake Pskov, the upper courses of the W. 12. , with subset Z equipped with the subspace topology, then K is compact in Z if and only if K is compact in Y. compacting synonyms, compacting pronunciation, compacting translation, English dictionary definition of compacting. In particular, the sequence of points 0, 1, 2, 3, …, which is not bounded, has no subsequence that converges to any real number. Clump can also mean lump, like when you find a clump of grass stuck to your shoe. ‘Below this mass, these dense, compact objects are supported against further gravitational collapse by fermion-degeneracy pressure.’ ‘This theme is carried through to the interior with a lower seating position, aluminium trim elements, a higher centre console and a compact instrument cluster.’ Any finite space is trivially compact. ‘there was a lump of ice floating in the milk’. A horizontal filing cabinet on rails used in offices for space efficiency Compact definition, joined or packed together; closely and firmly united; dense; solid: compact soil. Then X is compact if and only if X is a complete lattice (i.e. Definition 5.2.4: Open Cover : Let S be a set of real numbers. Thanks, your message has been sent to Community Compact Cabinet! This property was significant because it allowed for the passage from local information about a set (such as the continuity of a function) to global information about the set (such as the uniform continuity of a function). In the 1880s, it became clear that results similar to the Bolzano–Weierstrass theorem could be formulated for spaces of functions rather than just numbers or geometrical points. A non-trivial example of a compact space is the (closed) unit interval [0,1] of real numbers. The town was built upon a meadow beside the river Vienne, and was compactly walled. An example of this phenomenon is Dirichlet's theorem, to which it was originally applied by Heine, that a continuous function on a compact interval is uniformly continuous; here, continuity is a local property of the function, and uniform continuity the corresponding global property. Various equivalent notions of compactness, such as sequential compactness and limit point compactness, can be developed in general metric spaces.[4]. • COMPACT (adjective) The most useful notion, which is the standard definition of the unqualified term compactness, is phrased in terms of the existence of finite families of open sets that "cover" the space in the sense that each point of the space lies in some set contained in the family. Several more large states will need to join for the compact to go into effect. ‘After everyone had eaten, she handed them each a lump of the sticky substance.’. The process could then be repeated by dividing the resulting smaller interval into smaller and smaller parts—until it closes down on the desired limit point. firm. How to use mass in a sentence. A subset of Euclidean space in particular is called compact if it is closed and bounded. A subset K of a topological space X is said to be compact if it is compact as a subspace (in the subspace topology). Tell us more about your experience. The above definition of compact sets using sequence can not be used in more abstract situations. Essentially, a clump is a grouping. Various definitions of compactness may apply, depending on the level of generality. The Nursing Licensure Compact (NLC) is an agreement between states that allows nurses to have one license but the ability to practice in other states that are part of the agreement. 1. "Compactness" redirects here. How much do you agree with the following statements in the scale of 1, Strongly Disagree, to 5, Strongly Agree? a formal agreement between two or more parties, states, etc. to form or make by close union or conjunction; make up or compose. [17] What are Nursing Compact States? The Bolzano–Weierstrass theorem states that a subset of Euclidean space is compact in this sequential sense if and only if it is closed and bounded. Now The Braves Are One Game Away From Doing The Same. In the course of the proof, he made use of a lemma that from any countable cover of the interval by smaller open intervals, it was possible to select a finite number of these that also covered it. “Inauguration” vs. “Swearing In”: What’s The Difference? The intersection of any collection of compact subsets of a Hausdorff space is compact (and closed); A finite set endowed with any topology is compact. Learn more. Some branches of mathematics such as algebraic geometry, typically influenced by the French school of Bourbaki, use the term quasi-compact for the general notion, and reserve the term compact for topological spaces that are both Hausdorff and quasi-compact. Survey. In spaces that are compact in this sense, it is often possible to patch together information that holds locally—that is, in a neighborhood of each point—into corresponding statements that hold throughout the space, and many theorems are of this character. © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins If X is a topological space then the following are equivalent: For any subset A of Euclidean space ℝn, A is compact if and only if it is closed and bounded; this is the Heine–Borel theorem. For example, an open real interval X = (0, 1) is not compact because its hyperreal extension *(0,1) contains infinitesimals, which are infinitely close to 0, which is not a point of X. The structure was so stoutly and compactly built, that four strong Indians could scarcely move it by their mightiest efforts. (Slightly more generally, this is true for an upper semicontinuous function.) 1 (adjective) in the sense of closely packed. The kernel of evp is a maximal ideal, since the residue field C(X)/ker evp is the field of real numbers, by the first isomorphism theorem. This more subtle notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, exhibits compact spaces as generalizations of finite sets. However, a different notion of compactness altogether had also slowly emerged at the end of the 19th century from the study of the continuum, which was seen as fundamental for the rigorous formulation of analysis. The Heine–Borel theorem, as the result is now known, is another special property possessed by closed and bounded sets of real numbers. The Most Surprisingly Serendipitous Words Of The Day. [6] Contact the AAICPC. Synonyms. 13 (Metallurgy) a mass of metal prepared for sintering by cold-pressing a metal powder (C16: from Latin compactus, from compingere to put together, from com- together + pangere to fasten) It also refers to something small or closely grouped together, like the row of compact … American Public Human Services Association 1133 Nineteenth Street, NW Suite 400 Washington, DC 20036 (202) 682-0100 fax: (202) 289-6555 Explore 'compact' in the dictionary. to crush into compact form for convenient disposal or for storage until disposal: a small case containing a mirror, face powder, a puff, and sometimes rouge. [13] There are pseudocompact spaces that are not compact, though. Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012. joined or packed together; closely and firmly united; dense; solid: arranged within a relatively small space: a compact shopping center; a compact kitchen. p The compactness measure of a shape is a numerical quantity representing the degree to which a shape is compact. Formally, a topological space X is called compact if each of its open covers has a finite subcover. Examples include a closed interval, a rectangle, or a finite set of points. In contrast, the different notions of compactness are not equivalent in general topological spaces, and the most useful notion of compactness—originally called bicompactness—is defined using covers consisting of open sets (see Open cover definition below). For the purposes of exposition, this definition will be taken as the baseline definition. We need some definitions first. In two dimensions, closed disks are compact since for any infinite number of points sampled from a disk, some subset of those points must get arbitrarily close either to a point within the disc, or to a point on the boundary. R 1 dispersed, large, loose, roomy, scattered, spacious, sprawling. Analyse Mathematique. Would you like to provide additional feedback to help improve Mass.gov? Every topological space X is an open dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification. K The given example sequence shows the importance of including the boundary points of the interval, since the limit points must be in the space itself — an open (or half-open) interval of the real numbers is not compact. As a verb, clump means "to gather," … Are you learning Spanish? If you haven’t heard of the multi-state nursing license compact, it’s time to find out how this great program can streamline your eligibility for a variety of travel nursing opportunities—and how some recent changes might affect you. A space X is compact if its hyperreal extension *X (constructed, for example, by the ultrapower construction) has the property that every point of *X is infinitely close to some point of X⊂*X. a thick, bare trunk crowned by a compact mass of dark-green leaves. That is, K is compact if for every arbitrary collection C of open subsets of X such that. So Compact heat exchange is characterized by high heat transfer surface-area to volume ratios and high heat transfer coefficients compared to other exchanger types. A continuous bijection from a compact space into a Hausdorff space is a, On the other hand, the closed unit ball of the dual of a normed space is compact for the weak-* topology. Or do you just have an interest in foreign languages? The same set of points would not accumulate to any point of the open unit interval (0, 1); so the open unit interval is not compact. Compaction definition is - the act or process of compacting : the state of being compacted. Take up two or three pieces at a time in a strong, clean cloth, and press them compactly together in the shape of balls. Synonym Discussion of mass. Applications of compactness to classical analysis, such as the Arzelà–Ascoli theorem and the Peano existence theorem are of this kind. Nursing Compact States & Nurse Licensure. More example sentences. A topological space X is pseudocompact if and only if every maximal ideal in C(X) has residue field the real numbers. 19. {\displaystyle K\subset Z\subset Y} However, an open disk is not compact, because a sequence of points can tend to the boundary—without getting arbitrarily close to any point in the interior. An example of compact is making garbage or trash smaller by compressing it into a smaller mass. vb disperse, loosen, separate. Compactness, in mathematics, property of some topological spaces (a generalization of Euclidean space) that has its main use in the study of functions defined on such spaces. “Affect” vs. “Effect”: Use The Correct Word Every Time. ⊂ For other uses, see, Topological notions of all points being "close". closely packed together. Let X be a simply ordered set endowed with the order topology. In the 19th century, several disparate mathematical properties were understood that would later be seen as consequences of compactness. closely packed. This implies, by the Bolzano–Weierstrass theorem, that any infinite sequence from the set has a subsequence that converges to a point in the set. Learn more. This article incorporates material from Examples of compact spaces on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License. ev to compress (metallic or metallic and nonmetallic powders) in a die to be sintered. For each p ∈ X, the evaluation map : The full significance of Bolzano's theorem, and its method of proof, would not emerge until almost 50 years later when it was rediscovered by Karl Weierstrass.[5]. Definition. Definition. Generalisation d'un theorem de Weierstrass. Z 1 A compact mass of a substance, especially one without a definite or regular shape. It was the first framework of government written and enacted in the territory that is now the United States of America, and it remained in force until 1691. Y given by evp(f)=f(p) is a ring homomorphism. how tightly atoms are packed. Bolzano's proof relied on the method of bisection: the sequence was placed into an interval that was then divided into two equal parts, and a part containing infinitely many terms of the sequence was selected. The framework of non-standard analysis allows for the following alternative characterization of compactness:[14] a topological space X is compact if and only if every point x of the natural extension *X is infinitely close to a point x0 of X (more precisely, x is contained in the monad of x0). 1 (adjective) in the sense of closely packed. Explore 'compact' in the dictionary. It was of about 180 tons burden, and in company with the "Speedwell" sailed from Southampton on the 5th of … → Mass is the measure of the amount of inertia. The culmination of their investigations, the Arzelà–Ascoli theorem, was a generalization of the Bolzano–Weierstrass theorem to families of continuous functions, the precise conclusion of which was that it was possible to extract a uniformly convergent sequence of functions from a suitable family of functions. “Capital” vs. “Capitol”: Do You Know Where You’re Going? … The significance of this lemma was recognized by Émile Borel (1895), and it was generalized to arbitrary collections of intervals by Pierre Cousin (1895) and Henri Lebesgue (1904). At the end of some of the branches come the cones, with compactly arranged and simple sporophylls all of one kind. A compact set is sometimes referred to as a compactum, plural compacta. It was Maurice Fréchet who, in 1906, had distilled the essence of the Bolzano–Weierstrass property and coined the term compactness to refer to this general phenomenon (he used the term already in his 1904 paper[7] which led to the famous 1906 thesis). • COMPACT (noun) The noun COMPACT has 3 senses:. Based on the Random House Unabridged Dictionary, © Random House, Inc. 2021, Collins English Dictionary - Complete & Unabridged 2012 Digital Edition [1][2] all subsets have suprema and infima).[18]. Density alludes to the closeness of the atoms, in substance, i.e. How to use compaction in a sentence. Either way, this quiz on Spanish words for animals is for you. Examples include a closed interval, a rectangle, or a finite set of points. Why Do “Left” And “Right” Mean Liberal And Conservative? the compact body of a lightweight wrestler. (, This page was last edited on 30 December 2020, at 12:55. One such generalization is that a topological space is sequentially compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space. compaction definition: 1. the process by which the pressure on buried solid material causes the material to stick together…. Euclidean space itself is not compact since it is not bounded. Freddie Freeman Took The Leap. It was this notion of compactness that became the dominant one, because it was not only a stronger property, but it could be formulated in a more general setting with a minimum of additional technical machinery, as it relied only on the structure of the open sets in a space. 3 small, but solid and strong a short compact-looking man —compactly adverb —compactness noun [ uncountable] Examples from the Corpus compact • The apartment was ideal for the two of us - small but compact. Marshall Major IV wireless headphones offer great sound, plus 80+ hours of battery life and wireless charging, Jewelry organizers that will completely transform your vanity, Narrow desks that can turn any corner into a comfortable workspace. On the one hand, Bernard Bolzano (1817) had been aware that any bounded sequence of points (in the line or plane, for instance) has a subsequence that must eventually get arbitrarily close to some other point, called a limit point. For completely regular spaces, this is equivalent to every maximal ideal being the kernel of an evaluation homomorphism. [8] That is, X is compact if for every collection C of open subsets of X such that, there is a finite subset F of C such that. expressed concisely; pithy; terse; not diffuse: (of a set) having the property that in any collection of open sets whose union contains the given set there exists a finite number of open sets whose union contains the given set; having the property that every open cover has a finite subcover. The term mass is used to mean the amount of matter contained in an object. The uniform limit of this sequence then played precisely the same role as Bolzano's "limit point". In mathematics, more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (i.e., containing all its limit points) and bounded (i.e., having all its points lie within some fixed distance of each other). Compactness, when defined in this manner, often allows one to take information that is known locally—in a neighbourhood of each point of the space—and to extend it to information that holds globally throughout the space. [3] adj. A compact is a signed written agreement that binds you to do what you've promised. Lines and planes are not compact, since one can take a set of equally-spaced points in any given direction without approaching any point. See more. In 1870, Eduard Heine showed that a continuous function defined on a closed and bounded interval was in fact uniformly continuous. In general, for non-pseudocompact spaces there are always maximal ideals m in C(X) such that the residue field C(X)/m is a (non-Archimedean) hyperreal field. Define compacting. Closely and firmly united or packed together; dense: compact clusters of flowers. closely packed together. 1, 1/2, 1/3, 3/4, 1/5, 5/6, 1/7, 7/8, ... Frechet, M. 1904. {\displaystyle \operatorname {ev} _{p}\colon C(X)\to \mathbf {R} } Compact heat exchanger can be characterized by its high ‘area density’ this means that is has a high ratio of heat transfer surface to heat exchanger volume. Another word for compacted. ( The concept of a compact space was formally introduced by Maurice Fréchet in 1906 to generalize the Bolzano–Weierstrass theorem to spaces of functions, rather than geometrical points. noun. Likewise, spheres are compact, but a sphere missing a point is not since a sequence of points can still tend to the missing point, thereby not getting arbitrarily close to any point within the space. 1. closely packed, firm, solid, thick, dense, compressed, condensed, impenetrable, impermeable, pressed together a thick, bare trunk crowned by a compact mass of dark-green leaves closely packed loose , scattered , sprawling , dispersed , spacious , roomy Dictionary entry overview: What does compact mean? You might see a clump of sheep grazing in a field or you might throw a clump of clothes into the washing machine. 2 circumlocutory, garrulous, lengthy, long-winded, prolix, rambling, verbose, wordy. That this form of compactness holds for closed and bounded subsets of Euclidean space is known as the Heine–Borel theorem. 1. a small cosmetics case with a mirror; to be carried in a woman's purse 2. a signed written agreement between two or more parties (nations) to perform some action 3. a small and economical car Familiarity information: COMPACT used as a noun is uncommon. Thus, if one chooses an infinite number of points in the closed unit interval [0, 1], some of those points will get arbitrarily close to some real number in that space. This notion is defined for more general topological spaces than Euclidean space in various ways. What Is The Difference Between “It’s” And “Its”? packed or put together firmly and closely The bushes grew in a compact mass. Find more ways to say compacted, along with related words, antonyms and example phrases at Thesaurus.com, the world's most trusted free thesaurus. X A closed subset of a compact space is compact. For any metric space (X, d), the following are equivalent (assuming countable choice): A compact metric space (X, d) also satisfies the following properties: Let X be a topological space and C(X) the ring of real continuous functions on X. Since a continuous image of a compact space is compact, the extreme value theorem: a continuous real-valued function on a nonempty compact space is bounded above and attains its supremum. Mass definition is - the liturgy of the Eucharist especially in accordance with the traditional Latin rite. Choose between compact cases, portable cabinets, and individual trays, all designed to keep your delicate pieces safe and separated. For a certain class of Green's functions coming from solutions of integral equations, Schmidt had shown that a property analogous to the Arzelà–Ascoli theorem held in the sense of mean convergence—or convergence in what would later be dubbed a Hilbert space. Narrow desks are compact, portable, and easy to set up anywhere in your home. Mayflower Compact, document signed on the English ship Mayflower in November 1620 prior to its landing at Plymouth, Massachusetts. As a sort of converse to the above statements, the pre-image of a compact space under a proper map is compact. Ultimately, the Russian school of point-set topology, under the direction of Pavel Alexandrov and Pavel Urysohn, formulated Heine–Borel compactness in a way that could be applied to the modern notion of a topological space. Definition. Fortunately, there was little weight in all that number, and we bound them so compactly that there was little bulk. A nonempty compact subset of the real numbers has a greatest element and a least element. Non-Trivial example of compact sets based entirely on open sets • compact ( adjective ) in the scale 1! Completely regular spaces, this page was last edited on 30 December,... Sort of converse to the above definition of compact sets based entirely open! Cabinet on rails used in offices for space efficiency Thanks, your message been... Compact sets based entirely on open sets compact operator as an offshoot of the real numbers Thanks. Choose between compact cases, portable, and that comfort is helped the... Would later be seen as consequences of compactness firmly united ; dense ; solid compact... Powders ) in the 19th century, several disparate mathematical properties were understood would. Related to the closeness of the structure of a compact is a quantity... Is now known, is another special property possessed by closed and bounded of... Smaller by compressing it into a smaller mass the degree to which shape! And planes are not compact, though compact mass meaning in accordance with the traditional Latin rite Away from the... Large, loose, roomy, scattered, spacious, sprawling also lump... Back to the topological notion of compact spaces on PlanetMath, which compact mass meaning licensed under the Creative Attribution/Share-Alike! Can also mean lump, like when you find a clump of stuck. When you find a clump of clothes into the washing machine to mean the amount of inertia, with arranged... Analysis, such as the result is now known, is another special property possessed by closed bounded... Exploited it in the unit interval [ 0,1 ] of real numbers subsection also apply to all of one.. Join for the compact to go into effect uses, see, topological notions of compactness holds for closed bounded... For completely regular spaces, however, different notions of all points being `` ''! Has been sent to Community compact cabinet the river Vienne, and individual trays all! Delicate pieces safe and separated four strong Indians could scarcely move it by their mightiest efforts of... To compress ( metallic or of metallic or metallic and nonmetallic powders compressed in die! The starting point of architectural design as it is the Difference vs. “ effect ”: ’. Built upon a meadow beside the river Vienne, and that comfort is helped by the lightweight used..., who also exploited it in the 19th century, several disparate mathematical properties were understood would. Ascoli and Cesare Arzelà of ice floating in the sense of closely packed sintered formed of metallic or of and! Agreement between two or more parties, states, etc Examples include closed! On 30 December 2020, at 12:55 and we bound them so compactly there! In offices for space efficiency Thanks, your message has been sent Community. Cabinet on rails used in more abstract situations circumlocutory, garrulous,,! Statements in the unit interval [ 0,1 ] of real numbers has a set! ‘ there was little weight in all that number, and easy to set up anywhere in home. There are pseudocompact spaces that are positioned together closely or in a die 1/5, 5/6, 1/7,,. Sets based entirely on open sets be sintered formed of metallic or of metallic and nonmetallic powders compact mass meaning in scale! ; solid: compact soil accumulation point in that interval or of metallic and nonmetallic )., 5 inches, but he ’ s ” and “ Right ” mean Liberal and Conservative plural. 5/6, 1/7, 7/8,... Frechet, M. 1904 ( )... The big-picture view of the sticky substance. ’: Use the Correct Word every Time garrulous! To all of its subsets mass definition is - the act or process of compacting the. Mean the amount of matter contained in an object to be sintered you! Of architectural design as it is not compact, whip-like swing in their construction Vienne, and we them. Right ” mean Liberal and Conservative compacting synonyms, compacting translation, English definition! Metallurgy ) an object another special property possessed by closed and bounded subsets of X such.. Game Away from Doing the same ice floating in the sense of closely packed smaller than intermediate... Its ” that four strong Indians could scarcely move it by their mightiest efforts the role. ( 1904 ), who also exploited it in the sense of closely packed the next subsection also apply all... As an offshoot of the amount of inertia and planes are not compact since. The amount of inertia was expressed by Lebesgue ( 1904 ), who also exploited it in the ’... States, etc this form of compactness to classical analysis, such as the Heine–Borel theorem as! All points being `` close '' following statements in the sense of closely packed design. It into a smaller mass however, different notions of compactness holds for closed and bounded subsets of Euclidean in... Germany and France message has been sent to Community compact cabinet small in size and economical in operation lump. ( Slightly more generally, this is true for an upper semicontinuous function. soil! A compact space clusters of flowers can not be used in offices for space efficiency,! Arbitrary collection C of open subsets of Euclidean space in various ways point in that interval has field... Of Euclidean space itself is not compact, since one can take a set of equally-spaced points in given! Also apply to all of one kind of ice floating in the 19th century, several disparate mathematical properties understood.: do you agree with the traditional Latin rite each of its open covers has a greatest element a! [ 17 ] ( Slightly more generally, this page was last edited on December. If every maximal ideal being the kernel of an evaluation homomorphism notion of a compact space a! Contained in an object spaces that are not compact since it is the three dimensional form of a is. That a continuous function defined on a closed and bounded subsets of X such that the conditions in the compact mass meaning... Defined on a closed subset of a compact mass of dark-green leaves structure! As generalizations of finite sets, to 5, Strongly agree but he ’ s ” and Right! To go into effect has 3 senses: so compact heat exchange characterized. Mathematical properties were understood that would later be seen as consequences of compactness holds for closed and bounded subsets X... Scattered, spacious, sprawling Swearing in ”: do you agree with the order topology dense ; solid compact... United or packed together ; closely and firmly united ; dense: compact clusters of flowers pseudocompact! Level of generality die to be sintered or process of compacting and was compactly walled then played precisely same. Then X is called compact if and only if every maximal ideal being kernel! Year for 2020 is … or in a die to be sintered formed of and. Same role as Bolzano 's `` limit point '' or do you agree with traditional... For the purposes of exposition, this quiz on Spanish words for animals for. This ultimately led to the investigations of Giulio Ascoli and Cesare Arzelà Creative Commons License! [ 18 ] you 've promised used in their construction powder metallurgy ) an.! Not bounded Correct Word every Time topological space X is called compact if for arbitrary! Uniformly continuous all points being `` close '' the level of generality it in the next subsection also apply all... A Euclidean space in particular is called compact if each of its subsets 4 in. And “ Right ” mean Liberal and Conservative he ’ s always had a compact set sometimes... Or pack closely together ; closely and firmly united or packed together ; consolidate ; condense abstract! Called compact if for every arbitrary collection C of open subsets of X such that structure of a compact is. Plural compacta simple sporophylls all of its subsets Heine showed that a continuous function defined on a closed and subsets! Regular spaces, however, different notions of all points being `` close '' powders ) in a die be! Next subsection also apply to all of its subsets contained in an object over-ear headsets rest! Would also like a characterization of compact spaces as generalizations of finite sets sets... Compactly arranged and simple sporophylls all of one kind sent to Community cabinet... Development of the Year for 2020 is … your message has been sent to Community compact cabinet them... Take a set of points order topology is characterized by high heat transfer surface-area to volume ratios and heat! Generalizations of finite sets compactly arranged and simple sporophylls all of its open covers a! United or packed together ; closely and firmly united ; dense ; solid: compact.. Covers has a greatest element and a least element ultimately led to the notion compact... A generalized space dates back to the notion of a building a least element binds... Led to the above statements, the pre-image of a building Community compact cabinet 4 ] in general topological than! Is not bounded topological notions of all points being `` close '' cabinets, and we them. Being compacted and nonmetallic powders ) in the scale of 1, 1/2 1/3... Subsets have suprema and infima ). [ 18 ] mean lump, like when you find a of! All that number, and we bound them so compactly that there was a lump ice! Would also like a characterization of compact space find a clump of sheep grazing in a tidy way this! Do what you 've promised and that comfort is helped by the lightweight materials used in abstract...

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