On reflexivity and the Ascoli property for free locally convex spaces

S. Gabriyelyan

doi:10.1016/j.jpaa.2020.106413

On reflexivity and the Ascoli property for free locally convex spaces

S. Gabriyelyan

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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 language	American English
Article number	106413
Journal	Journal of Pure and Applied Algebra
Volume	224
Issue number	11
DOIs	https://doi.org/10.1016/j.jpaa.2020.106413
State	Published - 1 Nov 2020

Keywords

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jpaa.2020.106413

Cite this

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KW - Reflexive group

KW - The Ascoli property

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On reflexivity and the Ascoli property for free locally convex spaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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