Fixed point theorem in uniform spaces and applications
We study free topological groups defined over uniform spaces in some subclasses of the class of non-archimedean groups. Our descriptions of the corresponding topologies show that for metrizable uniformities the corresponding free balanced, free abelian and free Boolean groups are also metrizable. Graev type ultra-metrics determine the corresponding free topologies. Such results are in a striking contrast with free balanced and free abelian topological groups cases (in standard varieties). Another...
Following the paper [BDC1], further relations between the classical topologies on function spaces and new ones induced by hyperspace topologies on graphs of functions are introduced and further characterizations of boundedly spaces are given.