On the rigid covering fibrations

In 2002, Biss investigated on a kind of fibration which is called rigid covering fibration with properties similar to covering spaces. In this talk we obtain a relation between arbitrary topological spaces and its rigid covering fibrations. Specially, we show that if there exists a morphism f : EH  EG in the category of rigid covering fibrations of X, then H is a closed subgroup of G as subgroups of π1qtop (X).