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In [[mathematics]], a [[topological space]] is '''feebly compact''' if every [[locally finite collection|locally finite]] cover by nonempty [[open set]]s is finite. |
In [[mathematics]], a [[topological space]] is '''feebly compact''' if every [[locally finite collection|locally finite]] cover by nonempty [[open set]]s is finite. |
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Revision as of 01:35, 31 May 2020
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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.
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