Original scientific paper

A stronger limit theorem in extension theory

Leonard R. Rubin

Abstract

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 Xiτ|K|, then it is true that Xτ|K|, where X is the limit of the sequence. The property that Xτ|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 omly on the bonding maps, but one which is necessarily true in case each Xiτ|K|.

Keywords

Covering dimension; cohomological dimension; extension; limit; inverse sequence; metrizable space

Hrčak ID:

4853

URI

https://hrcak.srce.hr/4853

Publication date:

1.6.2001.

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