The orbit space of groupoids whose $C^{\ast }$-algebras are GCR

Abstract

Let $G$ be second countable locally compact Hausdorff groupoid with a continuous Haar system. We remove the assumption of amenability in a theorem by Clark about GCR groupoid $C^{\ast }$-algebras. We show that if the groupoid $C^{\ast }$-algebra of $G$ is GCR then the orbits of $G$ are locally closed.

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