Vol. 64, No. 1, 1976

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On certain point-countable covers

Dennis K. Burke and Ernest A. Michael

Vol. 64 (1976), No. 1, 79–92

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 xy, then 𝒫 has a finite subcollection such that x (∪ℱ) and y ∪ℱ.

Mathematical Subject Classification 2000
Primary: 54E35
Received: 24 November 1975
Published: 1 May 1976
Dennis K. Burke
Ernest A. Michael