Compactoid and compact filters

Szymon Dolecki, Gabriele H. Greco and Alois Andreas Lechicki

Vol. 117 (1985), No. 1, 69–98

DOI: 10.2140/pjm.1985.117.69

Abstract

We study compactoid and compact filters which generalize the concepts of convergent filters and compact sets. In particular, we investigate their properties in subregular and regular spaces, their localizations, and their countable variants. Several classical results follow (e.g., theorems of Tychonoff, Kuratowski, Choquet). More recent results on preservation of compactness (e.g., Smithson) and local compactness (e.g. Lambrinos) are extended and refined.

Mathematical Subject Classification 2000

Primary: 54D30

Secondary: 54A20, 90C48

Milestones

Received: 14 February 1983

Revised: 8 August 1983

Published: 1 March 1985