Monotonically normal e -separable spaces may not be perfect

John E. Porter

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 3, page 391-398
  • ISSN: 0010-2628

Abstract

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A topological space X is said to be e -separable if X has a σ -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.

How to cite

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Porter, John E.. "Monotonically normal $e$-separable spaces may not be perfect." Commentationes Mathematicae Universitatis Carolinae 59.3 (2018): 391-398. <http://eudml.org/doc/294321>.

@article{Porter2018,
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.},
author = {Porter, John E.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
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},
language = {eng},
number = {3},
pages = {391-398},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Monotonically normal $e$-separable spaces may not be perfect},
url = {http://eudml.org/doc/294321},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Porter, John E.
TI - Monotonically normal $e$-separable spaces may not be perfect
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 3
SP - 391
EP - 398
AB - 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.
LA - eng
KW - monotonically normal space; $\sigma $-closed-discrete dense set; $e$-separable space; perfect space; perfectly normal space; point network; perfect images of generalized ordered space
UR - http://eudml.org/doc/294321
ER -

References

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