Compactness (mathematics) | Properties of topological spaces

Feebly compact space

In mathematics, a topological space is feebly compact if every locally finite cover by nonempty open sets is finite. The concept was introduced by S. Mardeĉić and P. Papić in 1955. 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. (Wikipedia).

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Related pages

Compact space | Topological space | Locally finite collection | Mathematics | Pseudocompact space | Paracompact space | Hausdorff space | Open set