Glasnik Matematicki, Vol. 36, No.1 (2001), 95-103.

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 X_i each has the property that X_iτ|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 X_iτ|K|.

1991 Mathematics Subject Classification.   54F45, 55M15.

Key words and phrases.   Covering dimension, cohomological dimension, extension, limit, inverse sequence, metrizable space.