| Title:
|
Hausdorff topology and uniform convergence topology in spaces of continuous functions (English) |
| Author:
|
Artico, Umberto |
| Author:
|
Marconi, Giuliano |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
765-773 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The local coincidence of the Hausdorff topology and the uniform convergence topology on the hyperspace consisting of closed graphs of multivalued (or continuous) functions is related to the existence of continuous functions which fail to be uniformly continuous. The problem of the local coincidence of these topologies on ${}C(X,Y)$ is investigated for some classes of spaces: topological groups, zero-dimensional spaces, metric manifolds. (English) |
| Keyword:
|
hyperspace |
| Keyword:
|
Hausdorff metric and uniformity |
| Keyword:
|
metric manifold |
| MSC:
|
54A20 |
| MSC:
|
54B20 |
| MSC:
|
54C35 |
| MSC:
|
54E15 |
| idZBL:
|
Zbl 0853.54016 |
| idMR:
|
MR1378697 |
| . |
| Date available:
|
2009-01-08T18:21:32Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118803 |
| . |
| Reference:
|
[1] 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:
|
[2] Deimling K.: Nonlinear Functional Analysis.Springer-Verlag Berlin (1985). Zbl 0559.47040, MR 0787404 |
| Reference:
|
[3] Guillemin V., Pollack A.: Differential Topology.Prentice-Hall Inc. Englewood Cliffs NJ (1974). Zbl 0361.57001, MR 0348781 |
| Reference:
|
[4] Isbell J.R.: Uniform Spaces.Mathematical Surveys nr 12 AMS Providence, Rhode Island (1964). Zbl 0124.15601, MR 0170323 |
| Reference:
|
[5] Naimpally S.: Graph topology for function spaces.Trans. Amer. Math. Soc. 123 (1966), 267-272. Zbl 0151.29703, MR 0192466 |
| . |
