Correspondences of probability measures with restricted marginals revisited

We reprove a result of J. Bergin on the continuity of the correspondences of probability measures on a product space with restricted marginals. The proof is based on some functorial properties of probability measures. It works also for arbitrary number of coordinate spaces and for non-metrizable case.Probability measures on product spaces, Continuity of correspondence, Bicommutative diagram.

Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras

summary:We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described

Metrization of free groups on ultrametric spaces

AbstractWe consider ultrametrizations of free topological groups of ultrametric spaces. A construction is defined that determines a functor in the category UMET1 of ultrametric spaces of diameter ⩽1 and nonexpanding maps. This functor is the functorial part of a monad in UMET1 and we provide a characterization of the category of its algebras

Subpower Higson corona of a metric space

We define a subpower Higson corona of a metric space. This corona turns out to be an intermediate corona between the Higson corona and sublinear Higson corona. It is proved that the subpower compactification of an unbounded proper metric space contains a topological copy of the Stone-Cech compactification of a countable discrete space. We also provide an example of a map between geodesic spaces that is not asymptotically Lipschitz but that generates a continuous map of the corresponding subpower Higson coronas