Compactifications and cohomological dimension

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Abstract

The following theorems follow from results proved in the paper: Theorem 1. For each Abelian group G≠0 there is a separable metric space X such that dimGX≤3 and all Hausdorff compactifications X′ of Sn× X, n≥0, have cohomological dimension dimGX′ strictly greater than dimG(Sn×X). Theorem 2. If G≠0 is either a torsion group or G is torsion free and l={p|p· G=G, p prime} is infinite, then there is a separable metric space X such that dimGX=2 and all Hausdorff compactifications X′ of Sn×X, n≥0, have cohomological dimension dimGX′; strictly greater than dimG(Sn×X). © 1993.

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Dydak, J. (1993). Compactifications and cohomological dimension. Topology and Its Applications, 50(1), 1–10. https://doi.org/10.1016/0166-8641(93)90068-O

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