Algebraic topology: On some results of topological group space

Abstract

Our main interest in this work is to study on topological group and topological groupoid spaces. We give new some results of certain types for topological group which are source proper group space denoted by (SPHΓ-Space), for topological groupoid are source proper topological groupoid denoted by (SPHG-Space) and for H-Space (H,π, D) are source proper groupoid space , denoted by (SPHH-Space). The important point is to get relationship of SPHΓ, SPHG-Space and SPHH-Space.