The free product of topological groups being Hausdorff is Hausdorff --- a new proof

2010/07/28 by Guram Samsonadze, G. Samsonadze, Dali Zangurashvili +3
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #math.GN #msc:18A30 #msc:20E06 #msc:22A05

paper · pdf · doi:10.48550/arxiv.1007.4887

The proof of the main result of the paper uses the other mathematician's theorem (published in Dokl. Akad. Nauk SSSR) which turns out to be false

arxiv created 2019/05/02 · arxiv updated 2019/05/03

Abstract

The explicit description of the topology of the free product of topological groups being Hausdorff is given. In particular, it is shown that it coincides with the so-called X₀-topology for the corresponding colimit X in the category of topological spaces. Applying this fact, a new short proof of the well-known Graev's theorem asserting that the free product of topological groups being Hausdorff is Hausdorff is given.

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