Hausdorff tight groupoids generalised

We extend Exel’s ample tight groupoid construction to general locally compact étale groupoids in the Hausdorff case. Moreover, we show how inverse semigroups are represented in this way as ‘pseudobases’ of open bisections, thus yielding a duality which encompasses various extensions of the classic S...

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Bibliographic Details
Published in:Semigroup forum 2020-04, Vol.100 (2), p.399-438
Main Authors: Bice, Tristan, Starling, Charles
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Research Article
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Summary:We extend Exel’s ample tight groupoid construction to general locally compact étale groupoids in the Hausdorff case. Moreover, we show how inverse semigroups are represented in this way as ‘pseudobases’ of open bisections, thus yielding a duality which encompasses various extensions of the classic Stone duality.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-019-10027-y