Hereditarily closure-preserving collections and metrization-Reference-Cited by-同舟云学术

Hereditarily closure-preserving collections and metrization

Published:1975 Issue:2 Volume:51 Page:483-488
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Burke D.,Engelking R.,Lutzer D.

Abstract

In this paper we present a generalization of the Nagata-Smirnov metrization theorem. We prove that a regular T 1 {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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1975-051-02/S0002-9939-1975-0370519-6/S0002-9939-1975-0370519-6.pdf

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4. A necessary and sufficient condition for metrizability of a topological space;Smirnov, Yu.;Doklady Akad. Nauk SSSR (N.S.),1951

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