On reflexivity and the Ascoli property for free locally convex spaces

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let L(X) be the free locally convex space over a Tychonoff space X. If X is Dieudonné complete (for example, metrizable), then L(X) is a reflexive group if and only if X is discrete. We prove also that L(X) is an Ascoli space if and only if X is a countable discrete space.

Original languageEnglish
Article number106413
JournalJournal of Pure and Applied Algebra
Volume224
Issue number11
DOIs
StatePublished - 1 Nov 2020

Keywords

  • Dieudonné complete space
  • Free locally convex space
  • Reflexive group
  • The Ascoli property

ASJC Scopus subject areas

  • Algebra and Number Theory

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