| Title:
|
On $n$-thin dense sets in powers of topological spaces (English) |
| Author:
|
Bartoš, Adam |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
73-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subset of a product of topological spaces is called $n$-thin if every its two distinct points differ in at least $n$ coordinates. We generalize a construction of Gruenhage, Natkaniec, and Piotrowski, and obtain, under CH, a countable $T_3$ space $X$ without isolated points such that $X^n$ contains an $n$-thin dense subset, but $X^{n + 1}$ does not contain any $n$-thin dense subset. We also observe that part of the construction can be carried out under MA. (English) |
| Keyword:
|
dense set |
| Keyword:
|
thin set |
| Keyword:
|
$\kappa $-thin set |
| Keyword:
|
independent family |
| MSC:
|
54A35 |
| MSC:
|
54B10 |
| idZBL:
|
Zbl 06562197 |
| idMR:
|
MR3478340 |
| DOI:
|
10.14712/1213-7243.2015.148 |
| . |
| Date available:
|
2016-04-12T05:04:55Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144916 |
| . |
| Reference:
|
[En] Engelking R.: General Topology.revised and completed edition, Sigma series in pure mathematics, 6, Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[GNP] Gruenhage G., Natkaniec T., Piotrowski Z.: On thin, very thin, and slim dense sets.Topology Appl. 154 (2007), no. 4, 817–833. MR 2294630, 10.1016/j.topol.2006.08.007 |
| Reference:
|
[HG] Hutchison J., Gruenhage G.: Thin-type dense sets and related properties.Topology Appl. 158 (2011), no. 16, 2174–2183. MR 2831904, 10.1016/j.topol.2011.07.005 |
| Reference:
|
[Je] Jech T.: Set Theory.The Third Millennium Edition, revised and expanded, Springer, Berlin, 2002. Zbl 1007.03002, MR 1940513 |
| Reference:
|
[Pi] Piotrowski Z.: Dense subsets of product spaces.Questions Answers Gen. Topology 11 (1993), 313–320. MR 1234206 |
| . |
