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$ \sigma$-hereditarily closure-preserving $ k$-networks and $ g$-metrizability


Author: Yoshio Tanaka
Journal: Proc. Amer. Math. Soc. 112 (1991), 283-290
MSC: Primary 54E99; Secondary 54E35
DOI: https://doi.org/10.1090/S0002-9939-1991-1049850-6
MathSciNet review: 1049850
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Abstract: We show that a regular space is $ g$-metrizable if and only if it is a weakly first countable space with a $ \sigma $-hereditarily closure-preserving $ k$-network.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1049850-6
Keywords: Hereditarily closure-preserving collection, $ k$-network, weak base, $ g$-metrizable space
Article copyright: © Copyright 1991 American Mathematical Society

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