What does compact space mean?
Definitions for compact space
com·pact space
This dictionary definitions page includes all the possible meanings, example usage and translations of the word compact space.
Wiktionary
compact spacenoun
Any topological subset of Euclidean space that is a compact set
Wikidata
Compact space
In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite sequence of points sampled from the space must eventually, infinitely often, get arbitrarily close to some point of the space. There are several different notions of compactness, noted below, that are equivalent in good cases. The version just described is known as sequential compactness. The Bolzano–Weierstrass theorem gives an equivalent condition for sequential compactness when considering subsets of Euclidean space: a set then is compact if and only if it is closed and bounded. Examples include a closed interval or a rectangle. Thus if one chooses an infinite number of points in the closed unit interval, some of those points must get arbitrarily close to some real number in that space. For instance, some of the numbers 1/2, 4/5, 1/3, 5/6, 1/4, 6/7, … get arbitrarily close to 0. Note that the same set of points would not have, as an accumulation point, any point of the open unit interval; hence that space cannot be compact. Euclidean space itself is not compact since it is not bounded. In particular, 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.
Numerology
Chaldean Numerology
The numerical value of compact space in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of compact space in Pythagorean Numerology is: 7
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"compact space." Definitions.net. STANDS4 LLC, 2024. Web. 28 Apr. 2024. <https://www.definitions.net/definition/compact+space>.
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