Published 2007-07-25
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.
Copyright (c) 2025 Scientia Series A: Mathematical Sciences
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How to Cite
Ge, X. (2007). Some characterizations of locally separable Metrizable Spaces. Scientia Series A: Mathematical Sciences, 15, 61-65. https://doi.org/10.71712/
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.
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