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- nouncompactness (noun)
- the quality of being closely packed together:"the soil's compactness makes root penetration difficult"
- the quality of having all the necessary components or features neatly fitted into a small space:"I really like the compactness of this camera"
- conciseness of expression in speech or writing:"he is known for the brevity and compactness of his prose"
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Compact space - Wikipedia
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) … See more
In the 19th century, several disparate mathematical properties were understood that would later be seen as consequences of compactness. On the one hand, Bernard Bolzano (1817) had been aware that any bounded sequence … See more
Various definitions of compactness may apply, depending on the level of generality. A subset of Euclidean space in particular is called … See more
• A compact subset of a Hausdorff space X is closed.
• In any topological vector space (TVS), a compact subset is See moreAny finite space is compact; a finite subcover can be obtained by selecting, for each point, an open set containing it. A nontrivial example of … See more
• Any finite topological space, including the empty set, is compact. More generally, any space with a finite topology (only finitely many open sets) is … See more
Wikipedia text under CC-BY-SA license Compact Space | Brilliant Math & Science Wiki
What Does Compactness Really Mean? - Scientific …
WEBMay 25, 2017 · The real definition of compactness is that a space is compact if every open cover of the space has a finite subcover.
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Compactness | Hausdorff, Metric Spaces & Topology | Britannica
1.4: Compactness and Applications - University of Toronto …
COMPACTNESS | English meaning - Cambridge Dictionary
Metric Spaces: Compactness - Hobart and William Smith Colleges
COMPACTNESS | definition in the Cambridge English Dictionary
How to understand compactness? - Mathematics Stack Exchange
compactness noun - Definition, pictures, pronunciation and usage …
Compactness (Chapter 8) - Real Analysis - Cambridge University …
2.05 Compactness - University College London
Locally compact space - Wikipedia
Compact Space -- from Wolfram MathWorld
Showing that $[0,1]$ is compact - Mathematics Stack Exchange
On the definition of compactness - Mathematics Stack Exchange
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