Orbit spaces of proper equivariant absolute extensors (Q818389)

All spaces are assumed to be Tychonoff (completely regular and Hausdorff). The following is the main result of this paper. Theorem. Suppose \(G\) is a locally compact group, \(H\) is a closed normal subgroup of \(G\), and \(X\) is a proper \(G\)-space such that the \(H\)-orbits in \(X\) are metrizable. If \(X\) is G-ANE (G-ANE\( (n)\), \(n\geq 0)\) then the \(H\)-orbit space \(X/H\) is a G/H-ANE (G/H-ANE\((n))\). This result extends the author's earlier result proved in [Topology Appl. 146--147, 289--315 (2005); corrigendum ibid. 153, No. 7, 1100--1102 (2006; Zbl 1072.54014)] for the special case \(H=G\). An overall perspective of this theorem is appreciably obtained in the context of the author's earlier work cited in this paper.