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Fall 1995 On Dense Metrizable Subspaces of Topological Spaces
Ollie Nanyes
Missouri J. Math. Sci. 7(3): 123-128 (Fall 1995). DOI: 10.35834/1995/0703123


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.


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Ollie Nanyes. "On Dense Metrizable Subspaces of Topological Spaces." Missouri J. Math. Sci. 7 (3) 123 - 128, Fall 1995.


Published: Fall 1995
First available in Project Euclid: 17 December 2019

zbMATH: 1097.54508
MathSciNet: MR1455283
Digital Object Identifier: 10.35834/1995/0703123

Rights: Copyright © 1995 Central Missouri State University, Department of Mathematics and Computer Science


Vol.7 • No. 3 • Fall 1995
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