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May 2016 $\omega$-Jointly Metrizable Spaces
M. A. Al Shumrani
Missouri J. Math. Sci. 28(1): 25-30 (May 2016). DOI: 10.35834/mjms/1474295353

Abstract

A topological space $X$ is $\omega$-jointly metrizable if for every countable collection of metrizable subspaces of $X$, there exists a metric on $X$ which metrizes every member of this collection. Although the Sorgenfrey line is not jointly partially metrizable, we prove that it is $\omega$-jointly metrizable.

We show that if $X$ is a regular first countable $T_{1}$-space such that $X$ is the union of two subspaces one of which is separable and metrizable, and the other is closed and discrete, then $X$ is $\omega$-jointly metrizable.

Citation

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M. A. Al Shumrani. "$\omega$-Jointly Metrizable Spaces." Missouri J. Math. Sci. 28 (1) 25 - 30, May 2016. https://doi.org/10.35834/mjms/1474295353

Information

Published: May 2016
First available in Project Euclid: 19 September 2016

zbMATH: 1351.54004
MathSciNet: MR3549805
Digital Object Identifier: 10.35834/mjms/1474295353

Subjects:
Primary: 54A25
Secondary: 54B05

Rights: Copyright © 2016 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.28 • No. 1 • May 2016
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