# Compact space/Related Articles

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*See also changes related to Compact space, or pages that link to Compact space or to this page or whose text contains "Compact space".*

## Parent topics

- Topology [r]: A branch of mathematics that studies the properties of objects that are preserved through continuous deformations (such as stretching, bending and compression).
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- Topological space [r]: A mathematical structure (generalizing some aspects of Euclidean space) defined by a family of open sets.
^{[e]} - Open set [r]: In geometry and topology, a set that does not contain any of its boundary points.
^{[e]} - Closed set [r]: In geometry and topology, a set that contains its boundary; the complement of an open set.
^{[e]} - Bounded set [r]: A set for which there is a constant
*C*such that the norm of all elements in the set is less than*C*.^{[e]} - Heine–Borel theorem [r]: In Euclidean space of finite dimension with the usual topology, a subset is compact if and only if it is closed and bounded.
^{[e]} - Metric space [r]: Any topological space which has a metric defined on it.
^{[e]} - Totally bounded set [r]: A subset of a metric space with the property that for any positive radius it is coveted by a finite union of open balls of given radius.
^{[e]} - Sequentially compact space [r]: A topological space in which every sequence has a convergent subsequence.
^{[e]} - Continuity [r]: Property of a function for which small changes in the argument of the function lead to small changes in the value of the function.
^{[e]} - Extreme value theorem [r]:
*Add brief definition or description* - Pavel Sergeevich Aleksandrov [r]:
*Add brief definition or description* - Pavel Samuilovich Urysohn [r]:
*Add brief definition or description* - Tychonov theorem [r]: The Cartesian product of compact topological spaces is compact.
^{[e]} - Hausdorff space [r]:
*Add brief definition or description* - Compactification [r]: A compact space in which a given topological space can be embedded as a dense subset.
^{[e]} - Compactness axioms [r]: Properties of a toplogical space related to compactness.
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