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June 2008 Spaces with a d-Point-Discrete Weak Base
Shou Lin, Chuan Liu, Lewis D. Ludwig
Tsukuba J. Math. 32(1): 165-177 (June 2008). DOI: 10.21099/tkbjm/1496165196


In this paper $\sigma$-point-discrete weak bases are considered. Three necessary conditions that individually ensure that a space with a $\sigma$-point-discrete weak base has a s-compact-finite weak base are given. We show that $\sigma$-compact-finite weak bases are preserved by closed sequence-covering maps. It is shown that a space $X$ is metrizable if and only if $X^{\omega}$ has a $\sigma$-point-discrete weak base. Conditions are given to ensure when a paratopological group with $\sigma$-point-discrete weak base is metrizable. Several open questions are posed.


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Shou Lin. Chuan Liu. Lewis D. Ludwig. "Spaces with a d-Point-Discrete Weak Base." Tsukuba J. Math. 32 (1) 165 - 177, June 2008.


Published: June 2008
First available in Project Euclid: 30 May 2017

zbMATH: 1156.54015
MathSciNet: MR2433021
Digital Object Identifier: 10.21099/tkbjm/1496165196

Rights: Copyright © 2008 University of Tsukuba, Institute of Mathematics


Vol.32 • No. 1 • June 2008
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