New Separation Axioms in Generalized Bitopological Space

Abstract

The main purpose of this paper was to continue the study of separation axioms which is introduced in part I [1]. Whereas the part I [2] was devoted to the axioms $i$PT-ordered spaces, $i=0, 1, 2$, in the part II the axioms $\text{iPT}^{-}$ -ordered spaces, $i=3, 4, 5$ and $i$ $\text{PR}^{-}$-ordered spaces, $j=2, 3, 4$ are introduced and studied. Clearly, if $I=\{\$\}$ in these axioms, then the previous axioms [3] coincide with the present axioms. Therefore, the current work is a generalization of the previous one. In addition, the relationships between these axioms and the previous one axioms have been obtained. Some examples are given to illustrate the concepts. Moreover, some important results related to these separations have been obtained.