93 citations · 214 across the 18 of their papers we have counts for
20 papers
Countably compact groups having minimal infinite powers
Dikran Dikranjan, Vladimir Uspenskij
We answer the question, raised more than thirty years ago, on whether the power (G raised to the power omega) of a countably compact minimal Abelian group G is minimal, by showing…
Real-valued measurable cardinals and sequentially continuous homomorphisms
Vladimir Uspenskij
A.V.Arkhangel'skii asked in 1981 if the variety of topological groups generated by free topological groups on metrizable spaces coincides with the class of all topolo…
Is the free locally convex space nuclear?
Arkady Leiderman, Vladimir Uspenskij
Given a class of Banach spaces, a locally convex space (LCS) is called {\em multi-} if can be isomorphically embedded into a product of spaces that…
On epimorphisms in some categories of infinite-dimensional Lie groups
Vladimir G. Pestov, Vladimir V. Uspenskij
Let be a smooth compact connected manifold. Let $G=\mbox{Diff}\, X$ be the group of diffeomorphisms of , equipped with the -topology, and let be the stabilizer…
Projectively universal countable metrizable groups
Vladimir G. Pestov, Vladimir V. Uspenskij
We prove that there exists a countable metrizable topological group such that every countable metrizable group is isomorphic to a quotient of . The completion of is…
The dual space of precompact groups
M. Ferrer, S. Hernández, V. Uspenskij
For any topological group the dual object is defined as the set of equivalence classes of irreducible unitary representations of equipped with the Fell topology. I…
Precompact groups and property (T)
M. Ferrer, S. Hernández, V. Uspenskij
For any topological group the dual object is defined as the set of equivalence classes of irreducible unitary representations of equipped with the Fell topology. I…
On extremely amenable groups of homeomorphisms
Vladimir Uspenskij
A topological group is {\em extremely amenable} if every compact -space has a -fixed point. Let be compact and . We prove that the follo…
On metrizable enveloping semigroups
Eli Glasner, Michael Megrelishvili, Vladimir V. Uspenskij
When a topological group acts on a compact space , its enveloping semigroup is the closure of the set of -translations, , in the compact space . Assum…
Unitary representability of free abelian topological groups
Vladimir V. Uspenskij
For every Tikhonov space the free abelian topological group and the free locally convex vector space admit a topologically faithful unitary representation. For co…
Representations of residually finite groups by isometries of the Urysohn space
Vladimir G. Pestov, Vladimir V. Uspenskij
As a consequence of Kirchberg's work, Connes' Embedding Conjecture is equivalent to the property that every homomorphism of the group into the unitary gro…
A short proof of a theorem of Morton Brown on chains of cells
Vladimir Uspenskij
Suppose that a topological space is the union of an increasing sequence of open subsets each of which is homeomorphic to the Euclidean space . Then itself is homeomorp…
A compact group which is not Valdivia compact
Wieslaw Kubiś, Vladimir Uspenskij
A compact space is {\em Valdivia compact} if it can be embedded in a Tikhonov cube in such a way that the intersection is dense in , where is the sigma-pr…
The Urysohn universal metric space is homeomorphic to a Hilbert space
Vladimir Uspenskij
The Urysohn universal metric space U is characterized up to isometry by the following properties: (1) U is complete and separable; (2) U contains an isometric copy of every separab…
Compactifications of topological groups
Vladimir Uspenskij
Every topological group has some natural compactifications which can be a useful tool of studying . We discuss the following constructions: (1) the greatest ambit is…
A note on the precompactness of weakly almost periodic groups
Michael G. Megrelishvili, Vladimir G. Pestov, Vladimir V. Uspenskij
An action of a group on a compact space is called weakly almost periodic if the orbit of every continuous function on is weakly relatively compact in . We observe…
On universal minimal compact G-spaces
Vladimir Uspenskij
For every topological group G one can define the universal minimal compact G-space X=M_G characterized by the following properties: (1) X has no proper closed G-invariant subsets;…
The Roelcke compactification of groups of homeomorphisms
V. V. Uspenskij
Let X be a zero-dimensional compact space such that all non-empty clopen subsets of X are homeomorphic to each other, and let H(X) be the group of all self-homeomorphisms of X with…
A note on a question of R. Pol concerning light maps
V. V. Uspenskij
Let f:X -> Y be an onto map between compact spaces such that all point-inverses of f are zero-dimensional. Let A be the set of all functions u:X -> I=[0,1] such that $u[f^\leftarro…
On subgroups of minimal topological groups
V. V. Uspenskij
A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. The Roelcke uniformity (or lower uniformity) on a topological group is the greatest…