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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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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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