IPIP-separation axioms in ideal bitopological ordered spaces II

The main purpose of this paper was to continue the study of separation axioms which is introduced in part I (Kandil et al., 2015). Whereas the part I (Kandil et al., 2015) was devoted to the axioms IPTiIPTi-ordered spaces, i=0,1,2i=0,1,2, in the part II the axioms IPTiIPTi-ordered spaces, i=3,4,5i=3,4,5 and IPRjIPRj-ordered spaces, j=2,3,4j=2,3,4 are introduced and studied. Clearly, if I={ϕ}I={ϕ} in these axioms, then the previous axioms (Singal and Singal, 1971; Abo Elhamayel Abo Elwafa, 2009) 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.