Glasnik Matematicki, Vol. 36, No.1 (2001), 95-103.
A STRONGER LIMIT THEOREM IN EXTENSION THEORY
Leonard R. Rubin
Department of Mathematics, University of Oklahoma, 601 Elm Ave.,
Norman, OK 73019, USA
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
then it is true that
where X is the limit of the sequence. The property that
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
1991 Mathematics Subject Classification.
Key words and phrases. Covering dimension, cohomological
dimension, extension, limit, inverse sequence, metrizable space.
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