Mazur spaces.
Moscow spaces, Pestov-Tkačenko Problem, and -embeddings
We show that there exists an Abelian topological group such that the operations in cannot be extended to the Dieudonné completion of the space in such a way that becomes a topological subgroup of the topological group . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions to the...