| Title:
|
Attouch-Wets convergence and Kuratowski convergence on compact sets (English) |
| Author:
|
Piccione, Paolo |
| Author:
|
Sampalmieri, Rosella |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
551-562 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a locally connected, $b$-compact metric space and $E$ a closed subset of $X$. Let $\Bbb G$ be the space of all continuous real-valued functions defined on some closed subsets of $E$. We prove the equivalence of the ${\tau_{_{a\!w}}}$ and ${\tau^c_{_{\!K}}}$ topologies on $\Bbb G$, where $\tau_{_{a\!w}}$ is the so called {\sl Attouch-Wets\/} topology, defined in terms of uniform convergence of distance functionals, and ${\tau^c_{_{\!K}}}$ is the topology of Kuratowski convergence on compacta. (English) |
| Keyword:
|
function spaces |
| Keyword:
|
Kuratowski convergence |
| Keyword:
|
hyperspaces |
| MSC:
|
49J52 |
| MSC:
|
54C35 |
| MSC:
|
54C99 |
| idZBL:
|
Zbl 0844.54010 |
| idMR:
|
MR1364496 |
| . |
| Date available:
|
2009-01-08T18:20:08Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118784 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
