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.

Cosets, Domain theory, Filters, Inverse semigroups, Local compactness, Order structures, Patch topology, Stone duality, Étale groupoids
Semigroup Forum

Bice, T. (Tristan), & Starling, C. (2019). Hausdorff tight groupoids generalised. Semigroup Forum. doi:10.1007/s00233-019-10027-y