Some characterizations of locally separable Metrizable Spaces

Xun Ge

doi:10.71712/

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Published: 2025-08-08

DOI: https://doi.org/10.71712/

Keywords:

metrizable space, locally separable space, locally Lindel¨of space, locally countable base, \(\sigma\) -weakly hereditarily closure-preserving base.

Xun Ge

Department of Mathematics, College of Zhangjiagang, Jiangsu University of Science and Technology, Zhangjiagang, Jiangsu, 215600, P.R.China

Abstract

In this paper, we prove that a space \(X\) is a locally separable metrizable space iff \(X\) has a locally countable base, iff \(X\) is a locally Lindel¨of space with a \(\sigma\) -weakly hereditarily closure-preserving base.

Issue

Vol. 15 (2007)

Section

Articles

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Ge, X. (2025). Some characterizations of locally separable Metrizable Spaces. Scientia Series A: Mathematical Sciences, 15, 61-65. https://doi.org/10.71712/