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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_14712_1213_7243_2015_253,
     author = {Porter, John E.},
     title = {Monotonically normal $e$-separable spaces may not be perfect},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {391--398},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {2018},
     doi = {10.14712/1213-7243.2015.253},
     mrnumber = {3861561},
     zbl = {06940879},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.253/}
}
TY  - JOUR
AU  - Porter, John E.
TI  - Monotonically normal $e$-separable spaces may not be perfect
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2018
SP  - 391
EP  - 398
VL  - 59
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.253/
DO  - 10.14712/1213-7243.2015.253
LA  - en
ID  - 10_14712_1213_7243_2015_253
ER  - 
%0 Journal Article
%A Porter, John E.
%T Monotonically normal $e$-separable spaces may not be perfect
%J Commentationes Mathematicae Universitatis Carolinae
%D 2018
%P 391-398
%V 59
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.253/
%R 10.14712/1213-7243.2015.253
%G en
%F 10_14712_1213_7243_2015_253
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/

Cité par Sources :