A revised closed graph theorem for quasi-Suslin spaces

Title:

A revised closed graph theorem for quasi-Suslin spaces

Creator:

Ferrando, Juan Carlos, Kakol, J., and Lopez Pellicer, M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8f98e069-f7a1-47cc-826a-e4a60d8e6b5b
uuid:8f98e069-f7a1-47cc-826a-e4a60d8e6b5b

Subject:

$K$-analytic space, web space, and quasi-Suslin space

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1115-1122

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:4

Harvested from:

CDK

Metadata only:

false