The orbit spaces of groupoids whose $C^{\ast }$-algebras are CCR

Abstract

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

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