Sequentially compact space: Difference between revisions

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==Relation with other properties==
==Relation with other properties==
===Stronger properties===
* [[Compact space]]


===Weaker properties===
===Weaker properties===


* [[Countably compact space]]
* [[Limit point-compact space]]
* [[Limit point-compact space]]
==References==
===Textbook references===
* {{booklink|Munkres}}, Page 179 (formal definition)

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 sequentially compact if every sequence in it has a convergent subsequence.

Relation with other properties

Weaker properties

References

Textbook references

  • Topology (2nd edition) by James R. MunkresMore info, Page 179 (formal definition)