Monotonically normal $e$-separable spaces may not be perfect
Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 3, pp. 391-398.

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A topological space $X$ is said to be $e$-separable if $X$ has a $\sigma$-closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that $e$-separable PIGO spaces are perfect and asked if $e$-separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of $e$-separable monotonically normal spaces which are not perfect. Extremely normal $e$-separable spaces are shown to be stratifiable.
DOI : 10.14712/1213-7243.2015.253
Classification : 54B10, 54D15, 54G20
Keywords: monotonically normal space; $\sigma$-closed-discrete dense set; $e$-separable space; perfect space; perfectly normal space; point network; perfect images of generalized ordered space
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Porter, John E. Monotonically normal $e$-separable spaces may not be perfect. Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 3, pp. 391-398. doi : 10.14712/1213-7243.2015.253. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.253/

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