Cauchy G-spaces: Local convexity
Submitted: 2024-12-07
|Accepted: 2025-02-24
|Published: 2025-04-01
Copyright (c) 2025 Bernd Losert, Gary Richardson
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
Cauchy monoid, Cauchy continuous action, locally convex Cauchy space, completion
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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.
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