engleski

On rectangular inverse systems of topological spaces

For every cofinite inverse system of compact Hausdorff spaces X = (X, p', ), there exists a cofinite inverse system of compact polyhedra Z = (Z, r'', × T) and there are mappings u : X Z, (, ) × T, such that u p' = r'' u', for '. Moreover, for every , the mapping u : X Z = (Z, r'', T), given by the mappings u', T, is a limit of Z. If mappings p : X X form a limit p : X X, then the mappings v = u p : X Z form a limit v : X Z. An analogous result holds for cofinite inverse systems of topological spaces and ANR-resolutions (polyhedral resolutions).

inverse systems ; inverse limit ; compact Hausdorf ; polyhedron ; ANR

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