Extensorial properties of orbit spaces of proper group actions (Q1807568)

The author studies some extensorial and retraction properties for several classes of topological \(G\)-spaces. Thus, for a compact group \(G\), he denotes by \(G\)-A(N)E the class of all \(G\)-equivariant absolute (neighborhood) extensors for all metrizable \(G\)-spaces (this is a straightforward extension to the case of \(G\)-spaces of the ordinary A(N)E spaces. A main result is the following: Let \(G\) be a compact group and suppose that \(X\) is a \(G\)-A(N)E space such that all all \(G\)-orbits in \(X\) are metric. Then the orbit space \(X/G\) is an A(N)E space. The author also extends this sort of results to arbitrary locally compact almost connected proper group actions.