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 Sibe Mardešić 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.

References