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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Advances in Mathematics

Bice, T. (Tristan), & Starling, C. (2019). General non-commutative locally compact locally Hausdorff Stone duality. Advances in Mathematics, 341, 40–91. doi:10.1016/j.aim.2018.10.031