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A revised closed graph theorem for quasi-Suslin spaces
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1115-1122 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46A03, 46A30, 54C05, 54C14, 54D08
Keywords: $K$-analytic space; web space; quasi-Suslin space 
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     author = {Ferrando, J. C. and K\k{a}kol, J. and Lopez Pellicer, M.},
     title = {A revised closed graph theorem for {quasi-Suslin} spaces},
     journal = {Czechoslovak Mathematical Journal},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a19/}
}
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Ferrando, J. C.; Kąkol, J.; Lopez Pellicer, M. A revised closed graph theorem for quasi-Suslin spaces. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1115-1122. http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a19/

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