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Bibliographic Details
Main Authors: Clark, Lisa Orloff, Thompson, Ryan, Tolich, Ilija
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.02926
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Table of 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.