Abstract
In this paper we construct a functor ˆ : proTop ! proANR which extends Mardeysic correspondence that assigns to every metrizable space its canonical ANR-resolution. Such a functor allows one to deÞne the strong shape category of prospaces and, moreover, to deÞne a class of spaces, called strongly Þbered, that play for strong shape equivalences the role that ANR- spaces play for ordinary shape equivalences. In the last sec- tion we characterize SSDR-promaps, as deÞned by Dydak and Nowak, in terms of the strong homotopy extension property considered by the author.
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