Displaying similar documents to “Locally solid topologies on vector valued function spaces.”

Generalized precompactness and mixed topologies.

Jurie Conradie (1993)

Collectanea Mathematica

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The equicontinuous sets of locally convex generalized inducted limit (or mixed) topologies are characterized as generalized precompact sets. Uniformly pre-Lebesgue and Lebesgue topologies in normed Riesz spaces are investigated and it is shown that order precompactness and mixed topologies can be used to great advantage in the study of these topologies.

The Mackey-Arens theorem for non-locally convex spaces.

Jerzy Kakol (1990)

Collectanea Mathematica

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Let R be a subcategory of the category of all topological vector spaces. Let E be an element of R. The problem of the existence of the finest R-topology on E with the same continuous linear functionals as the original one is discussed. Remarks concerning the Hahn-Banach Extension Property are included.

Locally solid topologies on spaces of vector-valued continuous functions

Marian Nowak, Aleksandra Rzepka (2002)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a completely regular Hausdorff space and E a real normed space. We examine the general properties of locally solid topologies on the space C b ( X , E ) of all E -valued continuous and bounded functions from X into E . The mutual relationship between locally solid topologies on C b ( X , E ) and C b ( X ) ( = C b ( X , ℝ ) ) is considered. In particular, the mutual relationship between strict topologies on C b ( X ) and C b ( X , E ) is established. It is shown that the strict topology β σ ( X , E ) (respectively β τ ( X , E ) ) is the finest σ -Dini topology...