Abstract
At the present state of development of shape theory, it is natural to look for the shape theoretic analogs of classical theorems of homotopy theory. This chapter presents some recent work on two of such theorems—the Hurewicz and the Whitehead theorems. It is well known that shape theory was first introduced by K. Borsuk for compact metric spaces. Since then shape theories for various other classes of spaces have been developed. If one has in mind establishing theorems of the Hurewicz and Whitehead type, then the most suitable approach to shape theory appears to be the one based on pro-homotopy. This approach is an improvement of the ANR-system approach.
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