On topologized fundamental group and strong small transfer spaces

Abstract

?Suppose $H\leq \pi_{1}(X,x_{0})$?. ?In this paper?, ?we show that quotient topological groups are relative strong small loop transfer space which is related to a subgroup of $ \pi_{1}(X,x_{0})$?. ?After?, ?we study the connection between the concepts of semilocally $H$-connected and strong $H$-small loop transfer spaces?. ?finally?, ?we present conditions under which a special generalized covering subgroup is covering?.