Near-rings of continuous functions on compact abelian groups.
New algebras of functions on topological groups arising from G-spaces
For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urysohn space of diameter 1, we show that SUC(G) is trivial. We introduce the notion of fixed point on a class...
Noncompact semigroup actions.
Non-constant continuous maps of modifications of topological spaces
Non-locally compact Polish groups and two-sided translates of open sets
This paper is devoted to the following question. Suppose that a Polish group G has the property that some non-empty open subset U is covered by finitely many two-sided translates of every other non-empty open subset of G. Is then G necessarily locally compact? Polish groups which do not have the above property are called strongly non-locally compact. We characterize strongly non-locally compact Polish subgroups of in terms of group actions, and prove that certain natural classes of non-locally...
Notes on compact semigroups with identity.