Strong shape of compact Hausdorff spaces (Q1183657)

A strong shape category ssh(Cpt) of spaces having the strong shape of a compact Hausdorff space is developed, following Cathey's program. It is shown that every space belonging to Cpt has an ``improvement'' in the sense of S. Ferry, which lies in Cpt, but it need not be compact. With the help of this result, the author proves that the category ssh(Cpt) is isomorphic to a subcategory of the strong shape category constructed by Cathey and Segal for arbitrary spaces.