Glasnik Matematicki, Vol. 39, No.1 (2004), 155-170.


Sibe Mardešić

Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10002 Zagreb, P.O. Box 335, Croatia

Abstract.   For every cofinite inverse system of compact Hausdorff spaces X = (Xλ, pλλ', Λ), there exists a cofinite inverse system of compact polyhedra Z = (Zλτ, rλλ'ττ', Λ × T) and there are mappings uλτ : Xλ Zλτ, (λ, τ) Λ × T, such that uλτ pλλ' = rλλ'ττ' uλ'τ, for τ ≤ τ'. Moreover, for every λ Λ, the mapping uλ : Xλ Zλ = (Zλτ, rλλ'ττ', T), given by the mappings uλ'τ, τ T, is a limit of Zλ. If mappings pλ : X Xλ form a limit p : X X, then the mappings vλτ = uλτ pλ : X Zλτ form a limit v : X Z. An analogous result holds for cofinite inverse systems of topological spaces and ANR-resolutions (polyhedral resolutions).

2000 Mathematics Subject Classification.   54B35.

Key words and phrases.   Inverse system, rectangular inverse system, inverse limit, iterated inverse limit, compact Hausdorff space, compact metric space, polyhedron, ANR.

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