2023/09/23 by Sergey A. Antonyan, Antonyan, Sergey A.
Mathematics · #54C20 #54C55 #54H15 #57S20 #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2309.13491
openalex publication_date 2023/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a locally compact Hausdorff group. We study orbit spaces of equivariant absolute neighborhood extensors (G-\rm ANE's) for the class of all proper G-spaces that are metrizable by a G-invariant metric. We prove that if a G-space X is a G-\rm ANE and all G -orbits in X are metrizable, then the G-orbit space X/G is an \rm ANE. If G is either a Lie group or an almost connected group, then for any closed normal subgroup H of G, the H-orbit space X/H is a G/H-\rm ANE provided that all H-orbits in X are metrizable.