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

EXTENSION DIMENSION OF INVERSE LIMITS

Sibe Mardešić

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.