| Title:
|
Weak selections and flows in networks (English) |
| Author:
|
Gutev, Valentin |
| Author:
|
Nogura, Tsugunori |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
509-517 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We demonstrate that every Vietoris continuous selection for the hyperspace of at most 3-point subsets implies the existence of a continuous selection for the hyperspace of at most 4-point subsets. However, in general, we do not know if such ``extensions'' are possible for hyperspaces of sets of other cardinalities. In particular, we do not know if the hyperspace of at most 3-point subsets has a continuous selection provided the hyperspace of at most 2-point subsets has a continuous selection. (English) |
| Keyword:
|
hyperspace topology |
| Keyword:
|
Vietoris topology |
| Keyword:
|
continuous selection |
| Keyword:
|
flow |
| Keyword:
|
network |
| MSC:
|
05C90 |
| MSC:
|
05C99 |
| MSC:
|
54B20 |
| MSC:
|
54C65 |
| idZBL:
|
Zbl 1212.54034 |
| idMR:
|
MR2490443 |
| . |
| Date available:
|
2009-05-05T17:12:40Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119739 |
| . |
| Reference:
|
[1] Engelking R., Heath R.W., Michael E.: Topological well-ordering and continuous selections.Invent. Math. 6 (1968), 150-158. Zbl 0167.20504, MR 0244959, 10.1007/BF01425452 |
| Reference:
|
[2] García-Ferreira S., Gutev V., Nogura T.: Extensions of 2-point selections.New Zealand J. Math. (2006), to appear. MR 2491681 |
| Reference:
|
[3] Gutev V., Nogura T.: Selections and order-like relations.Appl. Gen. Topol. 2 (2001), 205-218. Zbl 0993.54019, MR 1890037 |
| Reference:
|
[4] Gutev V., Nogura T.: Some problems on selections for hyperspace topologies.Appl. Gen. Topol. 5 (2004), 1 71-78. MR 2087281 |
| Reference:
|
[5] Gutev V., Nogura T.: Selection problems for hyperspaces.Open Problems in Topology 2 (Elliott Pearl, ed.), Elsevier BV., Amsterdam, 2007, pp.161-170. MR 2367385 |
| Reference:
|
[6] Michael E.: Topologies on spaces of subsets.Trans. Amer. Math. Soc. 71 (1951), 152-182. Zbl 0043.37902, MR 0042109, 10.1090/S0002-9947-1951-0042109-4 |
| Reference:
|
[7] van Mill J., Wattel E.: Selections and orderability.Proc. Amer. Math. Soc. 83 (1981), 3 601-605. Zbl 0473.54010, MR 0627702, 10.1090/S0002-9939-1981-0627702-4 |
| . |
