A groupoid formulation of the Baire Category Theorem
Volume 226 / 2014
Fundamenta Mathematicae 226 (2014), 123-130
MSC: 03E25, 54E52, 22A22.
DOI: 10.4064/fm226-2-2
Abstract
We prove that the Baire Category Theorem is equivalent to the following: Let $G$ be a topological groupoid such that the unit space is a complete metric space, and there is a countable cover of $G$ by neighbourhood bisections. If $G$ is effective, then $G$ is topologically principal.
