Published 2007-07-05
Keywords
- metrizable space,
- locally separable space,
- locally Lindel¨of space,
- locally countable base,
- \(\sigma\) -weakly hereditarily closure-preserving base.
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How to Cite
Some characterizations of locally separable Metrizable Spaces. (2007). Scientia Series A: Mathematical Sciences, 15, 61-65. https://revistas.usm.cl/scientia/article/view/102
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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