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Pták homomorphism theorem revisited

J. R. FerrerM. López PellicerL. M. Sánchez Ruiz — 2000

Czechoslovak Mathematical Journal

Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.

A revised closed graph theorem for quasi-Suslin spaces

Juan Carlos FerrandoJ. KąkolM. Lopez Pellicer — 2009

Czechoslovak Mathematical Journal

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...

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