A Note on the Topology Associated with a Local Convex Space

Stojan Radenović

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Displaying similar documents to “A Note on the Topology Associated with a Local Convex Space”

A note on the topology associated with a locally convex space.

Radenović, Stojan (1986)

Publications de l'Institut Mathématique. Nouvelle Série

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On nonbornological barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

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If $E$ is the topological product of a non-countable family of barrelled spaces of non-nulle dimension, there exists an infinite number of non-bornological barrelled subspaces of $E$ . The same result is obtained replacing “barrelled” by “quasi-barrelled”.

Some examples on quasi-barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

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