| Title:
|
Further characterizations of boundedly UC spaces (English) |
| Author:
|
Holá, Ľubica |
| Author:
|
Holý, Dušan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
175-183 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Following the paper [BDC1], further relations between the classical topologies on function spaces and new ones induced by hyperspace topologies on graphs of functions are introduced and further characterizations of boundedly $\operatorname{UC}$ spaces are given. (English) |
| Keyword:
|
$\operatorname{UC}$ space |
| Keyword:
|
boundedly $\operatorname{UC}$ space |
| Keyword:
|
boundedly compact space |
| Keyword:
|
compact-open to\-po\-logy |
| Keyword:
|
topology of uniform convergence on bounded sets |
| Keyword:
|
Attouch-Wets topology |
| Keyword:
|
bounded proximal topology |
| MSC:
|
54C35 |
| MSC:
|
54E15 |
| MSC:
|
54F65 |
| idZBL:
|
Zbl 0828.54016 |
| idMR:
|
MR1240215 |
| . |
| Date available:
|
2009-01-08T18:02:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118567 |
| . |
| Reference:
|
[At] Atsuji M.: Uniform continuity of continuous functions of metric spaces.Pacific J. Math. 8 (1958), 11-16. Zbl 0082.16207, MR 0099023 |
| Reference:
|
[AW] Attouch H., Wets R.: Quantitative stability of variational systems I, The epigraphical distances.preprint. MR 1018570 |
| Reference:
|
[ALW] Attouch H., Lucchetti R., Wets R.: The topology of the $\rho $-Hausdorff distance.to appear in Annali Mat. Pure Appl. Zbl 0769.54009 |
| Reference:
|
[AP] Aze D., Penot J.: Operations on convergent families of sets and functions.Optimization 21 (1990), 521-534. Zbl 0719.49013, MR 1069660 |
| Reference:
|
[Be] Beer G.: Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance.Proc. Amer. Math. Soc. 95 (1985), 653-658. Zbl 0594.54007, MR 0810180 |
| Reference:
|
[BDC1] Beer G., DiConcilio A.: A generalization of boundedly compact metric spaces.Comment. Math. Univ. Carolinae 32 (1991), 362-367. MR 1137797 |
| Reference:
|
[BDC2] Beer G., DiConcilio A.: Uniform continuity on bounded sets and the Attouch-Wets topology.Proc. Amer. Math. Soc. 112 (1991), 235-244. MR 1033956 |
| Reference:
|
[BL1] Beer G., Lucchetti R.: Weak topologies for the closed subsets of a metrizable space.to appear in Trans. Amer. Math. Soc. Zbl 0810.54011, MR 1094552 |
| Reference:
|
[BL2] Beer G., Lucchetti R.: Well-posed optimization problems and a new topology for the closed subsets of a metric space.preprint. Zbl 0812.54015, MR 1256444 |
| Reference:
|
[BLLN] Beer G., Lechicki A., Levi S., Naimpally S.: Distance functionals and the suprema of hyperspace topologies.to appear in Annali Mat. Pure Appl. |
| Reference:
|
[Ho] Holá Ł.: The Attouch-Wets topology and a characterization of normable linear spaces.Bull. Austral. Math. Soc. 44 (1991), 11-18. MR 1120389 |
| Reference:
|
[LL] Lechicki A., Levi S.: Wijsman convergence in the hyperspace of a metric space.Bull. Un. Mat. Ital. 5-B (1987), 435-452. Zbl 0655.54007, MR 0896334 |
| Reference:
|
[Pe] Penot J.P.: The cosmic Hausdorff topology, the bounded Hausdorff topology, and continuity of polarity.to appear in Proc. Amer. Math. Soc. Zbl 0774.54008, MR 1068129 |
| . |
