Compactifications and cohomological dimension

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 dim GX≤3 and all Hausdorff compactifications X′ of S n× X, n≥0, have cohomological dimension dim GX′ strictly greater than dim G(S n×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 dim GX=2 and all Hausdorff compactifications X′ of S n×X, n≥0, have cohomological dimension dim GX′; strictly greater than dim G(S n×X).