Some topological properties weaker than compactness

G. Goss and Giovanni Viglino

Vol. 35 (1970), No. 3, 635–638

DOI: 10.2140/pjm.1970.35.635

Abstract

Many topological properties may be described by covering relations which may also generally be easily described in terms of filter relations. For example, a space is compact if and only if each open cover of the space contains a finite subcover, or equivalently, if each filter has an adherent point. In this paper, characterizations are given of some topological properties weaker than compactness, both in terms of filters and coverings. In the final section a question posed by Viglino and by Dickman and Zame is answered.

Mathematical Subject Classification

Primary: 54.52

Milestones

Received: 12 February 1970

Published: 1 December 1970