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Ivan Ivanšić ...et al KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.1
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.