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A Stronger Limit Theorem in Extension Theory
by
Leonard R. Rubin
Department of Mathematics, University of Oklahoma
This work contains an improvement to a limit theorem which has been proved by the author and P. J. Schapiro. In that result it was shown that for a given simplicial complex K, if an inverse sequence of metrizable spaces Xi each has the property that Xi\tau|K|, then it is true that X\tau|K|, where X is the limit of the sequence. The property that X\tau|K| means that for each closed subset A of X and each map f:A --> |K|, there exists a map F:X --> |K| which is an extension of f. This is the fundamental notion of extension theory.
The version put forth herein is stronger in that it places a requirement only on the bonding maps, but one which is necessarily true in case each Xi\tau|K|.
Date received: January 24, 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 # cady-09.