Feebly compact space
# 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.
