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
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
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