Topologically free non-Hausdorff groupoids
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910009856622592 |
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| author | Clark, Lisa Orloff Thompson, Ryan Tolich, Ilija |
| author_facet | Clark, Lisa Orloff Thompson, Ryan Tolich, Ilija |
| contents | We study three conditions that control the behaviour of isotropy in étale groupoids, and their relationships under the additional assumptions of second-countability and Hausdorffness. We examine a number of examples that show these properties are distinct. Working under the assumption of the Zermelo-Fraenkel axioms, excluding choice, we then examine an alternate characterization of topological freeness, first introduced by Anantharaman-Delaroche, in the non-Hausdorff setting. Finally, we prove an equivalence between the Baire Category Theorem and an étale groupoid theorem, along with similar equivalences to other weakenings of the Axiom of Choice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topologically free non-Hausdorff groupoids Clark, Lisa Orloff Thompson, Ryan Tolich, Ilija Operator Algebras Logic We study three conditions that control the behaviour of isotropy in étale groupoids, and their relationships under the additional assumptions of second-countability and Hausdorffness. We examine a number of examples that show these properties are distinct. Working under the assumption of the Zermelo-Fraenkel axioms, excluding choice, we then examine an alternate characterization of topological freeness, first introduced by Anantharaman-Delaroche, in the non-Hausdorff setting. Finally, we prove an equivalence between the Baire Category Theorem and an étale groupoid theorem, along with similar equivalences to other weakenings of the Axiom of Choice. |
| title | Topologically free non-Hausdorff groupoids |
| topic | Operator Algebras Logic |
| url | https://arxiv.org/abs/2602.02926 |