Partial actions on quotient spaces and globalization

Luis Martínez; Héctor Pinedo; Andrés Villamizar

doi:10.4995/agt.2024.17810

Authors

Luis Martínez Universidad Nacional Autónoma de México https://orcid.org/0000-0002-3957-3119
Héctor Pinedo Industrial University of Santander https://orcid.org/0000-0003-4432-419X
Andrés Villamizar University of Pamplona https://orcid.org/0009-0004-6458-644X

DOI:

https://doi.org/10.4995/agt.2024.17810

Keywords:

Topological partial action, G-equivalent spaces, Quotient space, G-invariant metric, orbit space

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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Author Biographies

Luis Martínez, Universidad Nacional Autónoma de México

Departamento de Matemáticas, Facultad de Ciencias

Héctor Pinedo, Industrial University of Santander

Escuela de Matemáticas, Facultad de Ciencias

Andrés Villamizar, University of Pamplona

Departamento de Matemáticas, Facultad de Ciencias Básicas

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