Topological spaces with a $\sigma$-point finite base
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- by C. E. Aull PDF
- Proc. Amer. Math. Soc. 29 (1971), 411-416 Request permission
Abstract:
The principal results of the paper are as follows. A topological space with a $\sigma$-point finite base has a $\sigma$-disjoint base if it is either hereditarily collectionwise normal or hereditarily screenable. From a metrization theorem of Arhangel’skiĭ, it follows that a ${T_1}$-space with a $\sigma$-point finite base is metrizable iff it is perfectly normal and collectionwise normal. A topological space with a $\sigma$-point base is quasi-developable in the sense of Bennett. Consequently a theorem of Čoban follows that for a topological space $(X,\Im )$ the following are equivalent: (a) $(X,\Im )$ is a metacompact normal Moore space, (b) $(X,\Im )$ is a perfectly normal ${T_1}$-space with a $\sigma$-point finite base.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 411-416
- MSC: Primary 54.50
- DOI: https://doi.org/10.1090/S0002-9939-1971-0281154-9
- MathSciNet review: 0281154