We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.

In this paper we study supremal representations positively homogeneous of degree one and symmetric positively homogeneous of degree two functions deened on a reeexive Banach space the Urysohn peak.

We give a survey of results and concepts related to certain problems on the Fréchet-Urysohn property in products. This material was presented in a workshop at the 2005 Summer Conference on Topology and its Applications at Denison University.

In this paper, we answer a question by Krasinkiewicz, Reńska and Sobolewski by constructing countable connected Hausdorff and Urysohn spaces as quotient spaces of bunches of arcs in the plane. We also consider a generalization of graphs by allowing vertices to be continua and replacing edges by not necessarily connected sets. We require only that two “vertices” be in the same quasi-component of...

We study properties of the automorphism groups of Fräıssé limits of classes with certain strong amalgamation properties, including classes with the free amalgamation property and classes of metric spaces. We discuss conditions on a Fräıssé class K that imply that the automorphism group GK of its limit admits generic elements of order n for all n and show that, for many such K, any element of GK...

We show that many countable groups acting on trees, including free products of infinitely and surface groups, are isomorphic to dense subgroups isometry bounded Urysohn spaces. This extends previous results the first t