Cell-like resolutions preserving cohomological dimensions
Abstract
We prove that for every compactum X with dimZ X <= n >= 2 there is a cell-like resolution r: Z --> X from a compactum Z onto X such that dim Z <= n and for every integer k and every abelian group G such that dimG X <= k >= 2 we have dimG Z <=k. The latter property implies that for every simply connected CW-complex K such that e-dim X <= K we also have e-dim Z <= K.
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