Continuity of semigroup actions.
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.
Continuous family groupoids.
Continuous homomorphisms on and Ramsey theory.
Continuous lattices and compact Lawson semilattices.
Continuously factorable groupoids.
Contraction semigroups and representations.
Contribution of noncommutative geometry to index theory on singular manifolds
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups [Book]
Controllability of systems on a nilpotent Lie group
Controllability on real reductive Lie groups.
Convergences for the group of real numbers
Convergent nets in abelian topological groups.
Convexity and almost convexity in groups
We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance...
Convolution semigroup of measures on compact noncommutative semigroups
Coproduct in the Category of Groups Satisfying Pontryagin Duality.
Correction to the paper “On compressed ideals in topological semigroups”
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