# Definition:Compact Space/Topology/Definition 5

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## Definition

A topological space $T = \left({S, \tau}\right)$ is **compact** if and only if every ultrafilter on $S$ converges.

## Also see

- Results about
**compact spaces**can be found**here**.

## Sources

There are no source works cited for this page.In particular: Recommend this page be removed as a "definition", and instead be converted to a proof that a compact space has this property.Source citations are highly desirable, and mandatory for all definition pages.Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |