Feebly compact space

Updated on Oct 27, 2023

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In mathematics, a topological space is feebly compact if every locally finite cover by nonempty open sets is finite.

Some facts:

Every compact space is feebly compact.

Every feebly compact paracompact space is compact.

Every feebly compact space is pseudocompact but the converse is not necessarily true.

For a completely regular Hausdorff space the properties of being feebly compact and pseudocompact are equivalent.

Any maximal feebly compact space is submaximal.

References

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