Norm upper-semicontinuity of functions supported on open abelian isotropy in étale groupoids. Corrigendum to “Reconstruction of groupoids and C⁎-rigidity of dynamical systems” [Adv. Math. 390 (2021) 107923]

Abstract

We consider étale Hausdorff groupoids in which the interior of the isotropy is abelian. We prove that the norms of the images under regular representations, of elements of the reduced groupoid $C^{⁎}$-algebra whose supports are contained in the interior of the isotropy vary upper semicontinuously. This corrects an error in [2].