Hereditarily closure-preserving collections and metrization
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- by D. Burke, R. Engelking and D. Lutzer PDF
- Proc. Amer. Math. Soc. 51 (1975), 483-488 Request permission
Abstract:
In this paper we present a generalization of the Nagata-Smirnov metrization theorem. We prove that a regular ${T_1}$-space is metrizable if and only if it has a base of open sets which is the union of countably many hereditarily closure-preserving subcollections. In addition, we investigate intersections of hereditarily closure-preserving collections of open sets.References
- Jack G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105–125. MR 131860
- I. Juhász, Cardinal functions in topology, Mathematical Centre Tracts, No. 34, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg. MR 0340021
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- Jun-iti Nagata, On a necessary and sufficient condition of metrizability, J. Inst. Polytech. Osaka City Univ. Ser. A 1 (1950), 93–100. MR 43448
- Yu. Smirnov, A necessary and sufficient condition for metrizability of a topological space, Doklady Akad. Nauk SSSR (N.S.) 77 (1951), 197–200 (Russian). MR 0041420
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 51 (1975), 483-488
- MSC: Primary 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1975-0370519-6
- MathSciNet review: 0370519