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Some examples on quasi-barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled 𝒟 -space containing a subspace of infinite countable codimension which is not 𝒟 -space, and bornological barrelled space which is not inductive limit of Baire space.

Some new classes of topological vector spaces with closed graph theorems

Brian Rodrigues (1991)

Commentationes Mathematicae Universitatis Carolinae

In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces. Our study includes a direct extension of Pták duality to the non-locally-convex situation.

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