Free abelian topological groups and collapsing maps

We show that for every pair (X,Y) of ANR compacta, Y⊂X, the free abelian topological group applied to a collapsing map q:X→X/Y produces a locally trivial bundle A(q):A(X)→A(X/Y) with the fiber A(Y). As a result we obtain a short proof of the classical Dold–Thom theorem which states that for all complexes X.