## Missouri Journal of Mathematical Sciences

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

### $\omega$-Jointly Metrizable Spaces

#### 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