| Title:
|
On dense subspaces satisfying stronger separation axioms (English) |
| Author:
|
Alas, Ofelia T. |
| Author:
|
Tkachenko, Mikhail G. |
| Author:
|
Tkachuk, Vladimir V. |
| Author:
|
Wilson, Richard G. |
| Author:
|
Yaschenko, Ivan V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
15-28 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than $c$ has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight $c$ which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of $\pi$-weight less than $\mathfrak p$ has a dense completely Hausdorff (and hence Urysohn) subspace. We show that there exists a Tychonoff space without dense normal subspaces and give other examples of spaces without “good” dense subsets. (English) |
| Keyword:
|
Hausdorff space |
| Keyword:
|
Urysohn space |
| Keyword:
|
completely Hausdorff space |
| Keyword:
|
filter of dense sets |
| MSC:
|
22A05 |
| MSC:
|
54C10 |
| MSC:
|
54C25 |
| MSC:
|
54D06 |
| MSC:
|
54D15 |
| MSC:
|
54D25 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1079.54518 |
| idMR:
|
MR1814628 |
| . |
| Date available:
|
2009-09-24T10:39:14Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127622 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
