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Hereditarily closure-preserving collections and metrization

Authors: D. Burke, R. Engelking and D. Lutzer
Journal: Proc. Amer. Math. Soc. 51 (1975), 483-488
MSC: Primary 54E35
MathSciNet review: 0370519
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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.

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Keywords: Metrizability, Nagata-Smirnov theorem, hereditarily closure-preserving collection
Article copyright: © Copyright 1975 American Mathematical Society

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