Partial actions on quotient spaces and globalization
Submitted: 2022-06-08
|Accepted: 2023-10-06
|Published: 2024-04-02
Copyright (c) 2024 Luis Martínez, Héctor Pinedo, Andrés Villamizar
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
Topological partial action, G-equivalent spaces, Quotient space, G-invariant metric, orbit space
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Abstract:
Given a partial action of a topological group G on a space X we determine properties P which can be extended from X to its globalization. We treat the cases when P is any of the following: Hausdorff, regular, metrizable, second countable, and having invariant metric. Further, for a normal subgroup H, we introduce and study a partial action of G/H on the orbit space of X; applications to invariant metrics and inverse limits are presented.
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