Cauchy G-spaces: Local convexity

Cauchy continuous actions of a Cauchy monoid acting on a locally convex Cauchy space X are investigated. The local convexity is determined by a partial order on X. Sufficient conditions are given to ensure the existence of a Hausdorff Cauchy space completion T for which the Cauchy continuous action can be appropriately extended to T.

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Publication Details

Journal
Applied General Topology
Published
2025-04-01
DOI
https://doi.org/10.4995/agt.2025.22992
Primary Topic
Advanced Topology and Set Theory
Type
article
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article

Cauchy G-spaces: Local convexity

Bernd Losert, G. D. Richardson
Applied General Topology
Advanced Topology and Set Theory
article

Cauchy G-spaces: Local convexity

Bernd Losert, G. D. Richardson
article en

Abstract

Cauchy continuous actions of a Cauchy monoid acting on a locally convex Cauchy space X are investigated. The local convexity is determined by a partial order on X. Sufficient conditions are given to ensure the existence of a Hausdorff Cauchy space completion T for which the Cauchy continuous action can be appropriately extended to T.

Applied General TopologyVol. 26(1)
University of Central Florida (US)
Openalex Percentile: Top 89%
Advanced Topology and Set Theory
DOIOpen Access PDFOpenAlex
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Cauchy G-spaces: Local convexity — Bernd Losert, G. D. Richardson · Applied General Topology (2025) | TGRS Research Map | TGRS