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


Leonard R. Rubin

Department of Mathematics, University of Oklahoma, 601 Elm Ave., Norman, OK 73019, USA e-mail:

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|.

1991 Mathematics Subject Classification.   54F45, 55M15.

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

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