A groupoid formulation of the Baire Category Theorem

TL;DR

This paper establishes an equivalence between the Baire Category Theorem and a property of topological groupoids, linking classical topology with groupoid theory through a new formulation.

Contribution

It introduces a groupoid-based formulation of the Baire Category Theorem, connecting topological groupoid properties with classical Baire category results.

Findings

Baire Category Theorem is equivalent to a property of effective topological groupoids.

Effective groupoids with certain covers are topologically principal.

Provides a new perspective linking topology and groupoid theory.

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.