In this paper, we introduced and studied a new kind of generalized closed set called τ1τ2-ḡ-closed set in a bitopological space (X, τ1, τ2). The properties of this τ1τ2-ḡ-closed set are studied and compared with some of the corresponding generalized closed sets in general topological spaces and bitopological spaces. We also defined the τ1τ2-ḡ-continuous function and studied some its properties.

In this paper, we introduced and studied a new kind of generalized open set called τ1τ2-g-open set in a bitopological space (X, τ1, τ2). The properties of this τ1τ2-g-open set are studied and compared with some of the corresponding generalized open sets in general topological spaces and bitopological spaces. We also dened the τ1τ2-g-continuous function and studied some its properties.

In this paper, we introduce the new concepts gr-compactness in topological spaces and obtain some of their properties using gr-closed sets.