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Baire-like spaces C(X,E)

Jerzy Kakol (2000)

Revista Matemática Complutense

We characterize Baire-like spaces Cc(X,E) of continuous functions defined on a locally compact and Hewitt space X into a locally convex space E endowed with the compact-open topology.

Barrelled spaces with Boolean rings of projections.

Lech Drewnowski (1997)

Collectanea Mathematica

The talk presented a survey of results most of which have been obtained over the last several years in collaboration with M.Florencio and P.J.Paúl (Seville). The results concern the question of barrelledness of locally convex spaces equipped with suitable Boolean algebras or rings of projections. They are particularly applicable to various spaces of measurable vector valued functions. Some of the results are provided with proofs that are much simpler than the original ones.

Barrelledness of generalized sums of normed spaces

Ariel Fernández, Miguel Florencio, J. Oliveros (2000)

Czechoslovak Mathematical Journal

Let ( E i ) i ∈ I be a family of normed spaces and λ a space of scalar generalized sequences. The λ -sum of the family ( E i ) i ∈ I of spaces is λ { ( E i ) i ∈ I } : = { ( x i ) i ∈ I , x i ∈ E i , and ( ∥ x i ∥ ) i ∈ I ∈ λ } . Starting from the topology on λ and the norm topology on each E i , a natural topology on λ { ( E i ) i ∈ I } can be defined. We give conditions for λ { ( E i ) i ∈ I } to be quasi-barrelled, barrelled or locally complete.

Biequivalence vector spaces in the alternative set theory

Miroslav Šmíd, Pavol Zlatoš (1991)

Commentationes Mathematicae Universitatis Carolinae

As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field Q of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total...

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