A revised closed graph theorem for quasi-Suslin spaces

Article

Abstract

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 {Aα:α ∈ ℕ} consisting of (relatively countably) compact sets such that AαAβ for αβ. Some applications and two open questions are provided.

Keywords

K-analytic space web space quasi-Suslin space 

MSC 2000

54C14 54D08 46A03 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.Centro de Investigación OperativaUniversidad Miguel HernándezElche (Alicante)Spain
  2. 2.Faculty of Mathematics and InformaticsA. Mickiewicz UniversityPoznańPoland
  3. 3.Depto. de Matemática Aplicada and IMPAUniversidad Politécnica de ValenciaValenciaSpain

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