Limit theorem for inverse sequences of metric spaces in extension theory
by
Leonard R. Rubin
University of Oklahoma
Coauthors: Philip J. Schapiro

We prove a limit theorem for extension theory for metric spaces. This theorem can be put in the following way. Suppose that K is a simplicial complex, |K| is given the weak topology, and a metrizable space X is the limit of an inverse sequence of metrizable spaces X_i having the property that X_i \tau|K| for each i in N. Then X \tau|K|. This latter property means that for each closed subset A of X and map f : A --> |K|, there exists a map F : X --> |K| which is an extension of f.

As a corollary to this we get the result of Nagami that the limit of an inverse sequence of metrizable spaces each having dimension <= n has dimension <= n. But we get much more, as this result extends to cohomological dimension modulo an abelian group. Hence, if G is an abelian group and X is the limit of an inverse sequence of metrizable spaces X_i where dim_G X_i <= n for each i in N, then dim_G X <= n.

Date received: February 9, 1997

Copyright © 1997 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 # caak-26.