Open AccessGeneralized ψ∗-closed sets in bitopological spaces
Author(s) -
H.M. Abu Donia,
M. A. Abd Allah,
Ashraf S. Nawar
Publication year - 2015
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2014.12.005
Subject(s) - mathematics , class (philosophy) , interpolation space , birnbaum–orlicz space , space (punctuation) , topological space , topological tensor product , pure mathematics , combinatorics , functional analysis , computer science , biochemistry , chemistry , artificial intelligence , gene , operating system
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