On certain point-countable covers

Dennis K. Burke and Ernest A. Michael

Vol. 64 (1976), No. 1, 79–92

DOI: 10.2140/pjm.1976.64.79

Abstract

In recent years, there have been a number of results about spaces with a point-countable cover satisfying various assumptions. In this paper, these results are generalized and unified by showing that the assumptions used can be significantly weakened. We are mostly concerned with consequences of the following condition: There is a point-countable cover 𝒫 of the space X such that, if x,y ∈ X with x≠y, then 𝒫 has a finite subcollection ℱ such that x ∈ (∪ℱ)^∘ and y∉ ∪ℱ.

Mathematical Subject Classification 2000

Primary: 54E35

Milestones

Received: 24 November 1975

Published: 1 May 1976