Compact space/Related Articles: Difference between revisions
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imported>Jitse Niesen (New page: {{subpages}} ==Parent topics== {{r|Topology}} <!-- ==Subtopics== List topics here that are included by this topic. --> ==Other related topics== {{r|Topological space}} {{r|Open set}} {{...) |
imported>Richard Pinch (→Other related topics: added Compactness axioms) |
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{{r|Metric space}} | {{r|Metric space}} | ||
{{r|Totally bounded set}} | {{r|Totally bounded set}} | ||
{{r|Sequentially compact | {{r|Sequentially compact space}} | ||
{{r|Continuity}} | {{r|Continuity}} | ||
{{r|Extreme value theorem}} | {{r|Extreme value theorem}} | ||
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{{r|Hausdorff space}} | {{r|Hausdorff space}} | ||
{{r|Compactification}} | {{r|Compactification}} | ||
{{r|Compactness axioms}} | |||
Revision as of 15:57, 30 October 2008
- 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). [e]
- 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]