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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-2-2,
author = {Jonathan Brown and Lisa Orloff Clark},
title = {A groupoid formulation of the Baire Category Theorem},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {123-130},
zbl = {06303623},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-2-2}
}
Jonathan Brown; Lisa Orloff Clark. A groupoid formulation of the Baire Category Theorem. Fundamenta Mathematicae, Tome 227 (2014) pp. 123-130. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-2-2/