2009/06/08 by Guram Samsonadze, Dali Zangurashvili, Samsonadze, Guram +1
Mathematics · #18A30 #20E06 #22A05 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CT #math.GN #msc:18A30 #msc:20E06 #msc:22A05
paper · pdf · doi:10.48550/arxiv.0906.1481
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
openalex publication_date 2009/06/08 · arxiv created 2019/05/02 · arxiv updated 2019/05/03 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The paper deals with the problem posed by Katz and Morris whether the free product with amalgamation of any Hausdorff topological groups is Hausdorff, the negative solution of which (even for the particular case of a closed amalgamated subgroup) easily follows from the relevant result by Uspenskij. The topology of such a product is characterized by proving that it coincides with the so-called X0-topology in the sense of Mal'tsev for the corresponding pushout X in the category of Hausdorff topological spaces. Applying this characterization, it is proved that the canonical mappings of Hausdorff groups into their amalgamated free product are open homeomorphic embeddings if an amalgamated subgroup is open. This immediately implies that in that case this product is Hausdorff.