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 | English |
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Article number | 106413 |
Journal | Journal of Pure and Applied Algebra |
Volume | 224 |
Issue number | 11 |
DOIs | |
State | Published - 1 Nov 2020 |
Keywords
- Dieudonné complete space
- Free locally convex space
- Reflexive group
- The Ascoli property
ASJC Scopus subject areas
- Algebra and Number Theory