Shape morphisms to transitive G-spaces (Q1810254)

A representation problem: Find conditions under which a shape morphism between two topological spaces is represented by a continuous mapping. This paper studies this problem in the context of equivariant shape theory. Here is the main result. Theorem. Suppose \(G\) is a compact and second countable topological group with a closed and normal subgroup \(H\). Put \(Y = G/H\). Then, any \(G\)-shape morphism from an arbitrary \(G\)-space \(X\) into \(Y\) can be represented by some equivariant mapping. Some interesting corollaries of this theorem are also stated.