Generalized ψ∗-closed sets in bitopological spaces

• Published in: Journal of the Egyptian Mathematical Society 2015-10, Vol.23 (3), p.527-534
• Main Authors: Abu Donia, H.M., Abd Allah, M.A., Nawar, A.S.
• Format: Article
• Language: English
• Subjects: [formula omitted] spaces; ij-T1/5 spaces; ij-T1/5ψ∗ spaces; ij-ψ∗-closed sets; ij-ψ∗-continuous functions; ij-ψ∗T1/5 spaces
• ISSN: 1110-256X; 2090-9128
• DOI: 10.1016/j.joems.2014.12.005

In this paper, we introduce and study a new class of sets in a bitopological space (X, τ1, τ2), 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-T1/5 spaces, ij-Te spaces, ij-αTe spaces, ij-Tl spaces and ij-αTl spaces. As applications of ij-ψ∗-closed sets, we introduce and study four new classes of spaces, namely, ij-T1/5ψ∗ spaces,ij-ψ∗T1/5 spaces (both classes contain the class of ij-T1/5 spaces), ij-αTk spaces and ij-Tk spaces. The class of ij-Tk spaces is properly placed in between the class of ij-Te spaces and the class of ij-Tl spaces. It is shown that dual of the class of ij-T1/2ψ∗ spaces to the class of ij-αTe spaces is the class of ij-αTk spaces and the dual of the class of ij-ψ∗T1/5 spaces to the class of ij-T1/5 spaces is the class of ij-T1/5ψ∗ spaces and also that the dual of the class of ij-Tl spaces to the class of ij-Tk spaces is the class of ij-αTk spaces. Further we introduce and study ij-ψ∗-continuous functions and ij-ψ∗-irresolute functions.