Published 28-02-2025
Keywords
- metrizable space,
- locally separable space,
- locally Lindel¨of space,
- locally countable base,
- \(\sigma\) -weakly hereditarily closure-preserving base.
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.
