In this paper we construct a functor $\Phi : \pT \to \pA$ which extends Marde\v si\' c correspondence that assigns to every metrizable space its canonical \A-resolution. Such a functor allows one to define the strong shape category of prospaces and, moreover, to define a class of spaces, called strongly fibered, that play for strong shape equivalences the role that \A-spaces play for ordinary shape equivalences. In the last section we characterize SSDR-promaps, as defined by Dydak and Nowak, in terms of the strong homotopy extension property considered by the author.
Homology, Homotopy and Applications, Vol. 4(2002), No. 1, pp. 71-85