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.

中文翻译：

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Hausdorff 紧群群广义化

我们在 Hausdorff 案例中将 Exel 充足的紧群群结构扩展到一般的局部紧凑 étale groupoids。此外，我们展示了逆半群如何以这种方式表示为开二分的“伪基”，从而产生包含经典斯通对偶性的各种扩展的对偶性。