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 GOspaces 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.
Original language | English |
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Pages (from-to) | 753-760 |
Number of pages | 8 |
Journal | Proceedings of the American Mathematical Society |
Volume | 101 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1987 |
Keywords
- Dense and codense example
- Metrizable
- Real go-space
- Totally metacompact
- Totally paracompact