## John E. PorterMonotonically normal $e$-separable spaces may not be perfect

Comment.Math.Univ.Carolin. 59,3 (2018) 391-398.

Abstract: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.

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

DOI: DOI 10.14712/1213-7243.2015.253
AMS Subject Classification: 54G20 54B10 54D15

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