Sigma-compact space: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[topological space]] is said to be '''sigma-compact''' or <math>\sigma</math>-compact if it has a countable collection of subsets such that the union of their interiors is the whole space. | A [[topological space]] is said to be '''sigma-compact''' or <math>\sigma</math>-compact if it has a countable collection of compact subsets such that the union of their interiors is the whole space. | ||
==Relation with other properties== | ==Relation with other properties== | ||
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Hemicompact space]] | |||
* [[Compact space]] | * [[Compact space]] | ||
* [[Manifold]] | |||
Latest revision as of 19:58, 11 May 2008
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This is a variation of compactness. View other variations of compactness
Definition
Symbol-free definition
A topological space is said to be sigma-compact or -compact if it has a countable collection of compact subsets such that the union of their interiors is the whole space.