In this note, the concepts of (G1,G2)-open, (G1,G2)-closed, (G1,G2)-quotient and (G1,G2)-perfect mappings on arbitrary sets are introduced some theorems them established firstly. particular, results improve corresponding in [17]. Secondly, we give a partial answer to question posed by L. Liu [14]. Finally, properties G-topological groups, G-connectedness totally G-disconnectedness groups discus...
