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A groupoid formulation of the Baire Category Theorem

Volume 226 / 2014

Jonathan Brown, Lisa Orloff Clark 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.

Authors

  • Jonathan BrownMathematics Department
    Kansas State University
    138 Cardwell Hall
    Manhattan, KS 66506-2602, U.S.A.
    e-mail
  • Lisa Orloff ClarkDepartment of Mathematics and Statistics
    University of Otago
    P.O. Box 56, Dunedin 9054, New Zealand
    e-mail

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