Mardesic Factorization Theorem for Extension Theory
by
Leonard Rubin
University of Oklahoma
Coauthors: Michael Levin, Phil Schapiro

We prove a Mardesi\' c factorization theorem for arbitrary extension theory in the class of compact Hausdorff spaces. Recall that if X is a compact Hausdorff space and K is a CW-complex, then X\tauK means that every map of a closed subset of X to K extends to a map of X to K. Our factorization theorem states that for every map f:X\rightaarrow Y of compact Hausdorff spaces, there exists a compact Hausdorff space Z and maps g:X --> Z, h:Z --> Y such that:

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(a)" wZ <= wY,

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(b)" h o g=f, and

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(c)" if K is a CW-complex and X\tauK, then Z\tauK.

Date received: January 20, 1998