Caractérisation des groupes de cohomologie d'un groupe topologique en termes de suites exactes
Closed subgroups in Banach spaces
We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of . Other results on subgroups of linear spaces are obtained.
Compact topologically torsion elements of topological abelian groups
Compactness type properties in topological groups
Complemented topologies on abelian groups.
Complements in the lattice of all topologies of topological groups
Complete -bounded groups need not be -factorizable
We present an example of a complete -bounded topological group which is not -factorizable. In addition, every -set in the group is open, but is not Lindelöf.
Completeness of sequential convergence groups
Condensations of Tychonoff universal topological algebras
Let be a Tychonoff (regular) paratopological group or algebra over a field or ring or a topological semigroup. If and , then there exists a Tychonoff (regular) topology such that and is a paratopological group, algebra over or a topological semigroup respectively.
Connected subgroups of nuclear spaces
Connectedness of complete metric groups
Connectivity in tl-groups
Continuous actions of pseudocompact groups and axioms of topological group
In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces that gives some new examples and statements for the -theory and theory of topologically homogeneous spaces.
Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups [Book]
Convergences for the group of real numbers
Convergent nets in abelian topological groups.
Coproduct in the Category of Groups Satisfying Pontryagin Duality.
Correction to the paper “The Bohr compactification, modulo a metrizable subgroup” (Fund. Math. 143 (1993), 119–136)
Countable dense homogeneous filters and the Menger covering property
We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any n ∈ ω ∪ {∞} an n-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.
Countable products of LCA groups: their closed subgroups, quotients and duality properties