Extension Shape Theory
by
Ivan Ivanšić
University of Zagreb
Coauthors: Leonard R. Rubin (University of Oklahoma), Philip J. Schapiro (University of Oklahoma)

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 \alpha, admit a P-invertible map of a compact Hausdorff space of weight <= \alpha and of extension dimension <= P onto the Tychonoff cube I^\alpha. 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.

Date received: March 14, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadz-93.