| Title:
|
A revised closed graph theorem for quasi-Suslin spaces (English) |
| Author:
|
Ferrando, J. C. |
| Author:
|
Kąkol, J. |
| Author:
|
Lopez Pellicer, M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
1115-1122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some results about the continuity of special linear maps between $F$-spaces recently obtained by Drewnowski have motivated us to revise a closed graph theorem for quasi-Suslin spaces due to Valdivia. We extend Valdivia's theorem by showing that a linear map with closed graph from a Baire tvs into a tvs admitting a relatively countably compact resolution is continuous. This also applies to extend a result of De Wilde and Sunyach. A topological space $X$ is said to have a (relatively countably) compact resolution if $X$ admits a covering $\{A_{\alpha }\:\alpha \in \Bbb N^{\Bbb N}\}$ consisting of (relatively countably) compact sets such that $A_{\alpha }\subseteq A_{\beta }$ for $\alpha \leq \beta $. Some applications and two open questions are provided. (English) |
| Keyword:
|
$K$-analytic space |
| Keyword:
|
web space |
| Keyword:
|
quasi-Suslin space |
| MSC:
|
46A03 |
| MSC:
|
46A30 |
| MSC:
|
54C05 |
| MSC:
|
54C14 |
| MSC:
|
54D08 |
| idZBL:
|
Zbl 1224.46004 |
| idMR:
|
MR2563582 |
| . |
| Date available:
|
2010-07-20T16:07:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140541 |
| . |
| Reference:
|
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| Reference:
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| . |
