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

ON RECTANGULAR INVERSE SYSTEMS OF TOPOLOGICAL SPACES

Sibe Mardešić

Abstract.   For every cofinite inverse system of compact Hausdorff spaces X = (X_λ, p_λλ', Λ), there exists a cofinite inverse system of compact polyhedra Z = (Z_λ^τ, r_λλ'^ττ', Λ × T) and there are mappings u_λ^τ : X_λ → Z_λ^τ, (λ, τ) ∈ Λ × T, such that u_λ^τ p_λλ' = r_λλ'^ττ' u_λ'^τ, for τ ≤ τ'. Moreover, for every λ ∈ Λ, the mapping u_λ : X_λ → Z_λ = (Z_λ^τ, r_λλ'^ττ', T), given by the mappings u_λ'^τ, τ ∈ T, is a limit of Z_λ. If mappings p_λ : X → X_λ form a limit p : X → X, then the mappings v_λ^τ = u_λ^τ p_λ : X → Z_λ^τ 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.