| Title:
|
Monotonically normal $e$-separable spaces may not be perfect (English) |
| Author:
|
Porter, John E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
391-398 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
monotonically normal space |
| Keyword:
|
$\sigma$-closed-discrete dense set |
| Keyword:
|
$e$-separable space |
| Keyword:
|
perfect space |
| Keyword:
|
perfectly normal space |
| Keyword:
|
point network |
| Keyword:
|
perfect images of generalized ordered space |
| MSC:
|
54B10 |
| MSC:
|
54D15 |
| MSC:
|
54G20 |
| idZBL:
|
Zbl 06940879 |
| idMR:
|
MR3861561 |
| DOI:
|
10.14712/1213-7243.2015.253 |
| . |
| Date available:
|
2018-09-10T12:19:01Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147406 |
| . |
| Reference:
|
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| Reference:
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| . |
