Abstract
In this note we investigate the question: when does the metrizability of a dense subspace of a topological space imply the metrizability of the whole space? We show that certain conditions always fail to be sufficient and then we examine some elementary examples. We conclude with a theorem which states that a first countable, regular, Hausdorff space $Y$ which has an open metrizable (in the subspace topology) subspace $X$ is metrizable provided $Y-X$ is scattered in $Y$. Our investigation is conducted on an elementary level.
Citation
Ollie Nanyes. "On Dense Metrizable Subspaces of Topological Spaces." Missouri J. Math. Sci. 7 (3) 123 - 128, Fall 1995. https://doi.org/10.35834/1995/0703123
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