Partial actions of groups on hyperspaces

[EN] Let X be a compact Hausdorff space. In this work we translate partial actions of X to partial actions on some hyperspaces determined by X, this gives an endofunctor 2- in the category of partial actions on compact Hausdorff spaces which generates a monad in this category. Moreover, structural relations between partial actions ? on X and partial determined by 2? as well as their corresponding globalizations are established.Martínez, L.; Tapia, HP.; Ramirez, E. (2022). Partial actions of groups on hyperspaces. Applied General Topology. 23(2):255-268. https://doi.org/10.4995/agt.2022.1574525526823

Partial actions of groups on profinite spaces

We show that for a partial action $\eta$ with closed domain of a compact group $G$ on a profinite space $X$ the space of orbits $X/\!\sim_G$ is profinite, this leads to the fact that when $G$ is profinite the enveloping space $X_G$ is also profinite. Moreover, we provide conditions for the induced quotient map $\pi_G: X\to X/\!\sim_G$ of $\eta$ to have a continuous section. Relations between continuous sections of $\pi_G$ and continuous sections of the quotient map induced by the enveloping action of $\eta$ are also considered. At the end of this work we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets

Partial actions on quotient spaces and globalization

Given a partial action of a topological group $G$ on a space $X$, we determine properties $\mathcal P$ which can be extended from $X$ to its globalization. We treat the cases when $\mathcal P$ 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 $X/\!\sim,$ applications to invariant metrics and inverse limits are presented.Comment: 14 page

Partial actions on quotient spaces and globalization

[EN] Given a partial action of a topological group G on a topological 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 actionof G/H on the orbit space X/∼H, applications to invariant metric sand inverse limits are presented.The first author was supported by CONAH-CYT (México).Martínez, L.; Tapia, HP.; Villamizar, A. (2024). Partial actions on quotient spaces and globalization. Applied General Topology. 25(1):125-141. https://doi.org/10.4995/agt.2024.1781012514125