On closed graph theorems in topological spaces and groups
On metrizable abelian groups with a completeness-type property
On solutions of the Gołab-Schinzel equation.
On the number of compact subsets in topological groups
On universal enveloping algebras in a topological setting
We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups...
Principle of equicontinuity for topological groups
Properties of quasi-invariant measures on topological groups and associated algebras
Seminormed spaces
Solution of distributive-like quasigroup functional equations
We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like quasigroup...
Summable families in nuclear groups
Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.
Sur certains espaces de fonctions dans les groupes localement compacts
The Clebsch-Gordan coefficients with respect to various bases for unitary and orthogonal representations of and .
The dual group of a dense subgroup
Throughout this abstract, is a topological Abelian group and is the space of continuous homomorphisms from into the circle group in the compact-open topology. A dense subgroup of is said to determine if the (necessarily continuous) surjective isomorphism given by is a homeomorphism, and is determined if each dense subgroup of determines . The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable group is...
The topological Hawaiian earring group does not embed in the inverse limit of free groups.
Topological groups and uniform continuity
Transforms associated to square integrable group representations. II : examples
Uniform measures on topological groups
Unitary closure and Fourier algebra of a topological group
This is a sequel to our recent work (2012) on the Fourier-Stieltjes algebra B(G) of a topological group G. We introduce the unitary closure G̅ of G and use it to study the Fourier algebra A(G) of G. We also study operator amenability and fixed point property as well as other related geometric properties for A(G).
Universal minimal flows of automorphism groups
Zum Satz vom abgeschlossenen Graphen in topologischen Gruppen.