Set-set topologies and semitopological groups (Q1823502)

Summary: Let G be a group with binary operation. Let T be a topology for G such that for all \(g\in G\) the maps, \(n_ g: G\to G\) and \({}_ gm: G\to G\), defined by \(m_ g(f)=f\cdot g\) and \({}_ gm(f)=g\cdot f\), respectively, are continuous. Then (G,T) is called a semitopological group. Some specific set-set topologies for function spaces are discussed and the concept of semitopologically determined collections of sets is introduced and used to classify some set-set topologies as semitopological groups.