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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Extension of Functions and \omega\mu-Metrizability
by
Ian Stares
Univ of North Carolina at Greensboro
Coauthors: Jerry Vaughan

A space X is said to have the Dugundji extension property (DEP) if for each closed subspace A of X there is a linear transformation \Phi: C(A) --> C(X) such that for each f in C(A), \Phi(f) extends f and the range of \Phi(f) is contained in the convex hull of the range of f. We present an example of an \omega\mu-metrizable space which does not have the DEP. This shows that van Douwen's result that all \omega\mu-metrizable spaces have the DEP and Borges' more general result that all linearly stratifiable spaces have the DEP are both incorrect. The example follows from a theorem providing general conditions under which the DEP may fail in normal spaces.

Date received: April 12, 1996

Copyright © 1996 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 # caaf-80.