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arXiv · 0812.4087

Non-Hausdorff groupoids

Ruy Exel
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Abstract

We present examples of non-Hausdorff, etale, essentially principal groupoids for which three results, known to hold in the Hausdorff case, fail. These results are: (A) the subalgebra of continuous functions on the unit space is maximal abelian within the reduced groupoid C*-algebra, (B) every nonzero ideal of the reduced groupoid C*-algebra has a nonzero intersection with the subalgebra of continuous functions on the unit space, and (C) the open support of a normalizer is a bissection.

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Ruy Exel. 2009-11-23. Non-Hausdorff groupoids. https://arxiv.org/abs/0812.4087

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