gm-continuity on generalized topology and minimal structure spaces

We introduce the concepts of gm-continuity, GM-converge to a point on generalized topology and minimal structure spaces. Also, we introduce the notions of gm-T2 space, gm-closed graph and strongly gm-closed graph on generalized topology and minimal structure spaces. We obtain several characterizations and properties of gm-continuous functions by using the interior operator and closure operator defined on both a generalized topology g and a minimal structure m. Moreover, we investigate some properties for gm-continuous functions by using the notions of gm-T2 space, gm-closed graph and strongly gm-closed graph.