Some Properties of Barrelled and of Bornological Locally Convex Spaces over an Arbitrary Complete Valued Field

V. Benekas
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V. Benekas: University of Ioannina

A chapter in Geometry and Non-Convex Optimization, 2025, pp 35-49 from Springer

Abstract: Abstract Without using the notion of convex, but strictly only absolutely convex, Barrelled and Bornological locally convex spaces over an arbitrary field, which has a valuation and is complete with the metric induced by the valuation, are being studied. As a continuation of a paper by the same author, it is proven that a barrelled space X is the strict inductive limit of an increasing sequence of subspaces whose union is X and if the sequence consists of bounded sets, X is a ( DF ) $$(DF)$$ -space. Bornological spaces also being studied. Two results analogous to barrelled spaces follow: a finite codimensional subspace of a bornological space remains bornological, and the same is true for quasibarrelled instead of bornological.

Date: 2025
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DOI: 10.1007/978-3-031-87057-6_2

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