| Title:
|
Locally solid topologies on spaces of vector-valued continuous functions (English) |
| Author:
|
Nowak, Marian |
| Author:
|
Rzepka, Aleksandra |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
473-483 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a completely regular Hausdorff space and $E$ a real normed space. We examine the general properties of locally solid topologies on the space $C_b(X,E)$ of all $E$-valued continuous and bounded functions from $X$ into $E$. The mutual relationship between locally solid topologies on $C_b(X,E)$ and $C_b(X)$ $(=C_b(X,\Bbb R))$ is considered. In particular, the mutual relationship between strict topologies on $C_b(X)$ and $C_b(X,E)$ is established. It is shown that the strict topology $\beta _\sigma(X,E)$ (respectively $\beta _\tau(X,E)$) is the finest $\sigma $-Dini topology (respectively Dini topology) on $C_b(X,E)$. A characterization of $\sigma $-Dini and Dini topologies on $C_b(X,E)$ in terms of their topological duals is given. (English) |
| Keyword:
|
vector-valued continuous functions |
| Keyword:
|
strict topologies |
| Keyword:
|
locally solid topologies |
| Keyword:
|
Dini topologies |
| MSC:
|
46A03 |
| MSC:
|
46E05 |
| MSC:
|
46E10 |
| MSC:
|
46E40 |
| MSC:
|
47A70 |
| idZBL:
|
Zbl 1068.46023 |
| idMR:
|
MR1920522 |
| . |
| Date available:
|
2009-01-08T19:24:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119336 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
