#### Glasnik Matematicki, Vol. 35, No.2 (2000), 339-354.

### EXTENSION DIMENSION OF INVERSE LIMITS

### Sibe Mardešić

Department of Mathematics, University of Zagreb, P.O. Box 335,
10002 Zagreb, Croatia

*e-mail:* `smarde@math.hr`

**Abstract.** Recently L.R. Rubin and P.J. Schapiro
have considered inverse sequences **X** of metrizable spaces
*X*_{i}, whose extension dimension
dim *X*_{i}
≤ *P*,
i.e., *P* ∈ AE(*X*_{i}),
where *P* is an arbitrary
polyhedron (or CW-complex). They proved that dim *X*
≤ *P*,
where *X* = lim **X**. The present paper generalizes
their result to inverse sequences of stratifiable spaces, giving at the
same time a more conceptual proof.

**1991 Mathematics Subject Classification.**
54B35, 54C55, 54F45.

**Key words and phrases.** Inverse limit, covering
dimension, cohomological dimension, extension theory,
extension dimension, metrizable space, stratifiable space.

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