I P -separation axioms in ideal bitopological ordered spaces II

Kandil, A.; Tantawy, O.; El-Sheikh, S. A.; Hosny, M.

doi:10.1016/j.joems.2015.05.004

I P -separation axioms in ideal bitopological ordered spaces II

Authors

¹ Department of Mathematics, Faculty of Science, Helwan University, Egypt

² Department of Mathematics, Faculty of Science, Zagazig University, Cairo, Egypt

³ Department of Mathematics, Faculty of Education, Ain Shams University, 11757 Beside Tabary School, Roxy, Cairo, Egypt

10.1016/j.joems.2015.05.004

Abstract

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 I PT i -ordered spaces, i = 0 , 1 , 2 , in the part II the axioms I PT i -ordered spaces, i = 3 , 4 , 5
and I PR j -ordered spaces, j = 2 , 3 , 4 are introduced and studied. Clearly, if 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 exam-
ples are given to illustrate the concepts. Moreover, some important results related to these separations
have been obtained

Keywords