A groupoid formulation of the Baire Category Theorem

Jonathan Brown; Lisa Orloff Clark

doi:10.4064/fm226-2-2

A groupoid formulation of the Baire Category Theorem

Jonathan Brown
, Lisa Orloff Clark

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	123-130
Number of pages	8
Journal	Fundamenta Mathematicae
Volume	226
Issue number	2
DOIs	https://doi.org/10.4064/fm226-2-2
State	Published - 1 Jan 2014
Externally published	Yes

Keywords

Baire category theorem
Effective groupoid
Principle of dependent choice
Topologically principal groupoid

ASJC Scopus subject areas

Algebra and Number Theory

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10.4064/fm226-2-2

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title = "A groupoid formulation of the Baire Category Theorem",

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.",

keywords = "Baire category theorem, Effective groupoid, Principle of dependent choice, Topologically principal groupoid",

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KW - Principle of dependent choice

KW - Topologically principal groupoid

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A groupoid formulation of the Baire Category Theorem

Abstract

Keywords

ASJC Scopus subject areas

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