Partial actions of groups on hyperspaces

TL;DR

This paper explores how partial group actions on compact spaces can be extended to hyperspaces, establishing a functor and monad structure, and analyzing their interrelations.

Contribution

It introduces a functor and monad for partial actions on hyperspaces derived from compact Hausdorff spaces, and studies their structural relations.

Findings

Defined a functor $2^{-}$ for partial actions on hyperspaces

Established a monad structure in the category of partial actions

Analyzed the relations between partial actions on $X$ and on hyperspaces

Abstract

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 $\theta$ on $X$ and partial determined by $2^{\theta}$ are established.