Sequentially compact space

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

• Countably compact space
• Limit point-compact space

References

Textbook references

• Topology (2nd edition) by James R. Munkres^{More info}, Page 179 (formal definition)