Spaces determined by point-countable covers

Gary Fred Gruenhage, Ernest A. Michael and Yoshio Tanaka

Vol. 113 (1984), No. 2, 303–332

DOI: 10.2140/pjm.1984.113.303

Abstract

Recall that a collection 𝒫 of subsets of X is point-countable if every x ∈ X is in at most countably many P ∈𝒫. Such collections have been studied from several points of view. First, in characterizing various kinds of s-images of metric spaces, second, to construct conditions which imply that compact spaces and some of their generalizations are metrizable, and finally, in the context of meta-Lindelöf spaces. This paper will make some contributions to all of these areas.

Mathematical Subject Classification 2000

Primary: 54D20

Secondary: 54C10, 54E99

Milestones

Received: 18 August 1982

Published: 1 August 1984