Generalized ψ∗-closed sets in bitopological spaces

Abstract

Abstract In this paper, we introduce and study a new class of sets in a bitopological space ( X , τ 1 , τ 2 ), namely, ij - ψ ∗ -closed sets, which settled properly in between the class of ji -α-closed sets and the class of ij -gα-closed sets. We also introduce and study new classes of spaces, namely, ij - T 1 / 5 spaces, ij - T e spaces, ij - αT e spaces, ij - T l spaces and ij - αT l spaces. As applications of ij - ψ ∗ -closed sets, we introduce and study four new classes of spaces, namely, ij - T 1 / 5 ψ ∗ spaces , ij - ψ ∗ T 1 / 5 spaces (both classes contain the class of ij - T 1 / 5 spaces), ij - αT k spaces and ij - T k spaces. The class of ij - T k spaces is properly placed in between the class of ij - T e spaces and the class of ij - T l spaces. It is shown that dual of the class of ij - T 1 / 2 ψ ∗ spaces to the class of ij - αT e spaces is the class of ij - αT k spaces and the dual of the class of ij - ψ ∗ T 1 / 5 spaces to the class of ij - T 1 / 5 spaces is the class of ij - T 1 / 5 ψ ∗ spaces and also that the dual of the class of ij - T l spaces to the class of ij - T k spaces is the class of ij - αT k spaces. Further we introduce and study ij - ψ ∗ -continuous functions and ij - ψ ∗ -irresolute functions.