| Title:
|
Weak orderability of some spaces which admit a weak selection (English) |
| Author:
|
Costantini, Camillo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
609-615 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that if a Hausdorff topological space $X$ satisfies one of the following properties: \noindent a) $X$ has a countable, discrete dense subset and $X^2$ is hereditarily collectionwise Hausdorff; \noindent b) $X$ has a discrete dense subset and admits a countable base; \noindent then the existence of a (continuous) weak selection on $X$ implies weak orderability. As a special case of either item a) or b), we obtain the result for every separable metrizable space with a discrete dense subset. (English) |
| Keyword:
|
weak (continuous) selection |
| Keyword:
|
weak orderability |
| Keyword:
|
Vietoris topology |
| Keyword:
|
dense countable subset |
| Keyword:
|
isolated point |
| Keyword:
|
countable base |
| Keyword:
|
collectionwise Hausdorff space |
| MSC:
|
54C65 |
| MSC:
|
54D15 |
| MSC:
|
54D70 |
| MSC:
|
54E35 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1150.54020 |
| idMR:
|
MR2337415 |
| . |
| Date available:
|
2009-05-05T16:59:56Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119621 |
| . |
| Reference:
|
[1] Artico G., Marconi U., Pelant J., Rotter L., Tkachenko M.: Selections and suborderability.Fund. Math. 175 1-33 (2002). Zbl 1019.54014, MR 1971236 |
| Reference:
|
[2] Engelking R.: General Topology.Heldermann Verlag, Berlin, revised and completed edition, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[3] García-Ferreira S., Gutev V., Nogura T., Sanchis M., Tomita A.: Extreme selections for hyperspaces of topological spaces.Topology Appl. 122 157-181 (2002). Zbl 1034.54007, MR 1919299 |
| Reference:
|
[4] García-Ferreira S., Sanchis M.: Weak selections and pseudocompactness.Proc. Amer. Math. Soc. 132 1823-1825 (2004). Zbl 1048.54012, MR 2051146 |
| Reference:
|
[5] Gutev V., Nogura T.: A topology generated by selections.Topology Appl. 153 (2005), 900-911. Zbl 1089.54005, MR 2203899 |
| Reference:
|
[6] Michael E.: Topologies on spaces of subsets.Trans. Amer. Math. Soc. 71 152-182 (1951). Zbl 0043.37902, MR 0042109 |
| Reference:
|
[7] van Mill J., Wattel E.: Selections and orderability.Proc. Amer. Math. Soc. 83 601-605 (1981). Zbl 0473.54010, MR 0627702 |
| . |
