Missouri Journal of Mathematical Sciences

$\omega$-Jointly Metrizable Spaces

M. A. Al Shumrani

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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.

Article information

Source
Missouri J. Math. Sci., Volume 28, Issue 1 (2016), 25-30.

Dates
First available in Project Euclid: 19 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1474295353

Digital Object Identifier
doi:10.35834/mjms/1474295353

Mathematical Reviews number (MathSciNet)
MR3549805

Zentralblatt MATH identifier
1351.54004

Subjects
Primary: 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80}
Secondary: 54B05: Subspaces

Keywords
$JPM$-space $\omega$-jointly metrizable space

Citation

Al Shumrani, M. A. $\omega$-Jointly Metrizable Spaces. Missouri J. Math. Sci. 28 (2016), no. 1, 25--30. doi:10.35834/mjms/1474295353. https://projecteuclid.org/euclid.mjms/1474295353


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References

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