On continuity of transversal maps and incomparable topologies for topological groups

Abstract

This article is devoted to a transversal map continuity on a topological group G. For the topological group G its proper nontrivial subgroups Gk are taken Gk⊂G, Gk≠G. In G relative to Gk the transversal set VG,Gk=Vk is considered. The coarsest topologies TG;Gk,Vk on G are studied relative to which the transversal maps τGkG:G→Vk are continuous and (G,TG;Gk,Vk) is the topological group. Then incomparable topologies on G are investigated with the help of transversal maps.