Locally Hausdorff Tight Groupoids Generalised

TL;DR

This paper generalizes the construction of tight groupoids from ample to non-ample, locally Hausdorff groupoids, broadening the applicability of the theory in operator algebras.

Contribution

It extends Exel's ample tight groupoid construction to the more general setting of locally Hausdorff, non-ample groupoids.

Findings

Successfully generalizes the tight groupoid construction.

Applicable to a wider class of groupoids.

Enhances understanding of groupoid C*-algebras.

Abstract

We extend Exel's ample tight groupoid construction to non-ample groupoids, even in the general locally Hausdorff case.