Compact space/Related Articles

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

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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). ^[e]

Other related topics

• 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. ^[e]