Total paracompactness of real GO-spaces

Authors:
Zoltán T. Balogh and Harold Bennett

Journal:
Proc. Amer. Math. Soc. **101** (1987), 753-760

MSC:
Primary 54F05; Secondary 54D18

DOI:
https://doi.org/10.1090/S0002-9939-1987-0911046-2

MathSciNet review:
911046

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Abstract: A topological space is said to be totally paracompact (resp. totally metacompact) if every open base of it has a locally finite (resp. pointfinite) subcover. In this paper we characterize all totally paracompact GO-spaces constructed on the real line. It turns out that in the class of GO-spaces on the real line, total paracompactness and total metacompactness are equivalent. Another consequence of our characterization is that totally metacompact GO-spaces on the real line are metrizable. Questions and partial results are given concerning total paracompactness in subspaces of real GO-spaces.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0911046-2

Keywords:
Real GO-space,
totally paracompact,
totally metacompact,
dense and codense example,
metrizable

Article copyright:
© Copyright 1987
American Mathematical Society