On the continuity of partial actions of Hausdorff groups on metric spaces

Jorge Gómez,Carlos Uscátegui,Héctor Pinedo

doi:10.15446/recolma.v1n52.74521

Jorge Gómez, Carlos Uscátegui + Show 1 more

Open Access

https://doi.org/10.15446/recolma.v1n52.74521

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Abstract

Proporcionamos condiciones suficientes para que una acción parcial separadamente continua de un grupo de Hausdorff en un espacio métrico sea continua.

Highlights

The notion of partial action of a group is a weakening of the classical concept of group action
Partial actions have been an important tool in C∗-algebras and dynamical systems, and in the construction of new cohomological theories [6], [5] and [12]
A partial action m : G ∗ X → X induces a family of bijections {mg : Xg−1 → Xg}g∈G

Summary

Introduction

The notion of partial action of a group is a weakening of the classical concept of group action. It was introduced in [7] and [4], and developed in [1] and [11], in which the authors provided examples in different guises. Every partial action of a group G on a set X can be obtained, roughly speaking, as a restriction of a global action (see [1] and [11]) on some bigger set XG, called the enveloping space of X. It is known that an action of a Polish group G on a metric space X is continuous provided that it is separately continuous (see for instance [8, Theorem 3.1.4]). Under a mild restriction, we generalize that result in two directions: First, we only assume that G is Hausdorff and Baire, and second, G acts partially on X

The notions

Topological partial actions of Hausdorff groups on metric spaces