Kandil, A., Tantawy, O., El-Sheikh, S., Hosny, M. (2016). I P -separation axioms in ideal bitopological ordered spaces II. test, 24(2), 279-285. doi: 10.1016/j.joems.2015.05.004
A. Kandil; O. Tantawy; S. A. El-Sheikh; M. Hosny. "I P -separation axioms in ideal bitopological ordered spaces II". test, 24, 2, 2016, 279-285. doi: 10.1016/j.joems.2015.05.004
Kandil, A., Tantawy, O., El-Sheikh, S., Hosny, M. (2016). 'I P -separation axioms in ideal bitopological ordered spaces II', test, 24(2), pp. 279-285. doi: 10.1016/j.joems.2015.05.004
Kandil, A., Tantawy, O., El-Sheikh, S., Hosny, M. I P -separation axioms in ideal bitopological ordered spaces II. test, 2016; 24(2): 279-285. doi: 10.1016/j.joems.2015.05.004

I P -separation axioms in ideal bitopological ordered spaces II

Journal of the Egyptian Mathematical Society
Volume 24, Issue 2, 2016, Pages 279-285    PDF (585.72 K)
DOI: 10.1016/j.joems.2015.05.004
Authors
A. Kandil1; O. Tantawy2; S. A. El-Sheikh3; M. Hosny3
1Department of Mathematics, Faculty of Science, Helwan University, Egypt
2Department of Mathematics, Faculty of Science, Zagazig University, Cairo, Egypt
3Department of Mathematics, Faculty of Education, Ain Shams University, 11757 Beside Tabary School, Roxy, Cairo, Egypt
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
Ideal bitopological ordered spaces; I-increasing ( I-decreasing) sets; IP-regular ordered spaces; IP-normal ordered spaces; IP-completely normal ordered spaces
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