General non-commutative locally compact locally Hausdorff Stone duality

We extend the classical Stone duality between zero dimensional compact Hausdorff spaces and Boolean algebras. Specifically, we simultaneously remove the zero dimensionality restriction and extend to étale groupoids, obtaining a duality with an elementary class of inverse semigroups.

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2019-01, Vol.341, p.40-91
Main Authors: Bice, Tristan, Starling, Charles
Format: Article
Language:English
Subjects:
Basis
Inverse semigroup
Rather below
Stone space
Topology
Étale groupoid
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Description
Summary:We extend the classical Stone duality between zero dimensional compact Hausdorff spaces and Boolean algebras. Specifically, we simultaneously remove the zero dimensionality restriction and extend to étale groupoids, obtaining a duality with an elementary class of inverse semigroups.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2018.10.031