Mappings on the dyadic solenoid
Answering an open problem in [3] we show that for an even number , there exist no to mappings on the dyadic solenoid.
Means of translates
Metrization criteria for compact groups in terms of their dense subgroups
According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or -dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined by all its...
Minimal Topological Groups.