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

TL;DR

This paper establishes a sufficient condition under which a separately continuous partial action of a Hausdorff group on a metric space is actually continuous, enhancing understanding of partial group actions.

Contribution

It introduces a new criterion that guarantees the continuity of partial actions from separate continuity in the context of Hausdorff groups and metric spaces.

Findings

A sufficient condition for continuity of partial actions.

Separately continuous partial actions can be continuous under certain conditions.

Improved understanding of the structure of partial group actions.

Abstract

We provide a sufficient condition for a topological partial action of a Hausdorff group on a metric space is continuous, provide that it is separately continuous.