Abstract
Recently Mardešić and Kozlowski, independently, have given a categorical description of shape for arbitrary topological spaces based on the concept of natural transformations of homotopy classes of maps into polyhedra. This chapter discusses the Kozlowski's work on generalizing movability to arbitrary topological spaces. This definition agrees with the original definition on compact metric spaces but it is stronger on compact Hausdorff spaces. The chapter presents a natural transformation approach to shape theory. For compacta movability, in the sense of Mardešić-Segal and property M are equivalent. Moreover, it is shown that for metric compacta property M and movability are equivalent.
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