engleski

Extension Shape Theory

We develop a theory of P-shape for the class of compact Hausdorff spaces and for certain CW-complexes P. The complexes P which are allowed are those which, for each given weight α , admit a P- invertible map of a compact Hausdorff space of weight ≤ α and of extension dimension ≤ P onto the Tychonoff cube I α . In particular it will be seen that classical shape theory comes from the case P = {;pt};. Our concept is based on extension theory, and hence for any extension equivalent CW-complex P’, P-shape and P’-shape will be identical. Indeed, if the extension theories of P and P’ are related so that P ≤ P’, then we shall obtain a relation between their shape functors, one factoring through the other.

extension theory ; dimension theory ; shape theory ; fundamental dimension ; movability

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