in this paper we construct the category of coverings of fundamental generalized lie group-groupoid associatedwith a connected generalized lie group. we show that this category is equivalent to the category of coverings of aconnected generalized lie group. in addition, we prove the category of coverings of generalized lie groupgroupoidand the category of actions of this generalized lie group-gro...

In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits of groups with topological approach.

The aim of this paper is to construct functors associated with topological groups as well as to investigate these functors. More precisely, we prove that for a given topological groups G there always exists a contravariant functor F (G) from the homotopy category of pointed topological spaces and homotopy classes of base point preserving continuous maps to the category of groups and homomorphis...

Abstract The purpose of this paper is to introduce ‐maps (), which describe higher homotopy normalities, and study their basic properties examples. An ‐map defined with homotopical conditions. It shown that a homomorphism an if only there exists fiberwise maps between projective spaces some properties. Also, the quotient be ‐space its LS category not greater than . As application, we investigat...