Atlas: Limit Theorem for Inverse Sequences of Metric Spaces in Extension Theory by Philip J. Schapiro

Atlas home || Conferences | Abstracts | about Atlas

The 1997 Spring Topology and Dynamics Conference
April 10-12, 1997
University of Southwestern Louisiana
Lafayette, LA, USA

Organizers
Bradd Clark, Kathleen Lopez, Vic Schneider, Roger Waggoner, Thelma West

View Abstracts

Limit Theorem for Inverse Sequences of Metric Spaces in Extension Theory
by
Philip J. Schapiro
Langston University
Coauthors: Leonard R. Rubin (Langston University)

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: March 14, 1997