#### 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
*e-mail:* `lrubin@ou.edu`

**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*_{i}τ|*K*|,
then it is true that
*X*τ|*K*|,
where *X* is the limit of the sequence. The property that
*X*τ|*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*_{i}τ|*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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