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

In: Geometry and Non-Convex Optimization

Author

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  • V. Benekas

    (University of Ioannina)

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.

Suggested Citation

  • V. Benekas, 2025. "Some Properties of Barrelled and of Bornological Locally Convex Spaces over an Arbitrary Complete Valued Field," Springer Optimization and Its Applications, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Geometry and Non-Convex Optimization, pages 35-49, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-87057-6_2
    DOI: 10.1007/978-3-031-87057-6_2
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