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Simply -factorizable (para)topological groups and their completions
Li-Hong Xie, Mikhail Tkachenko
Let us call a (para)topological group \emph{strongly submetrizable} if it admits a coarser separable metrizable (para)topological group topology. We present a characterization of s…
On convergent sequences in dual groups
M. V. Ferrer, S. Hernández, M. Tkachenko
We provide some characterizations of precompact abelian groups whose dual group endowed with the pointwise convergence topology on elements of contains a nontr…
The Separable Quotient Problem for Topological Groups
Arkady G. Leiderman, Sidney A. Morris, Mikhail G. Tkachenko
The famous Banach-Mazur problem, which asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient Banach space, has remained unsolved for 85 yea…
Lattices of homomorphisms and pro-Lie groups
Arkady G. Leiderman, Mikhail G. Tkachenko
Early this century K. H. Hofmann and S. A. Morris introduced the class of pro-Lie groups which consists of projective limits of finite-dimensional Lie groups and proved that it con…
Pontryagin duality in the class of precompact Abelian groups and the Baire property
Montserrat Bruguera, Mikhail Tkachenko
We present a wide class of reflexive, precompact, non-compact, Abelian topological groups determined by three requirements. They must have the Baire property, satisfy the \text…