on generalized covering subgroups of a fundamental group

 

in this talk, after reviewing concepts of covering, semicovering and generalized covering subgroups introduced by j. brazas, we give a new criterion for a subgroup h ≤ p1(x, x0) to be a generalized covering subgroup. recently, the notion of covering space has been extended using eliminating some of its properties and keeping some others. for instance, semicoverings are introduced by eliminating the evenly covered property and keeping local homeomorphismness and unique path lifting property. in the case of generalized coverings, local homeomorphismness has been replaced with unique lifting property.