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.

In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.

In this paper, we first discuss about canonical dual of g<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font...