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...

In this note‎, ‎we aim to show that several known generalizations of frames are equivalent to the continuous frame‎ ‎defined by Ali et al‎. ‎in 1993‎. ‎Indeed‎, ‎it is shown that these generalizations can be considered as an operator between two Hilbert spaces‎.