Open AccessAuthor(s) -
A. Kandil,
O. A. Tantawy,
S. A. El-Sheikh,
Mona Hosny
Publication year - 2016
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.2015.05.004
Subject(s) - axiom , generalization , mathematics , discrete mathematics , mathematical economics , mathematical analysis , geometry
AbstractThe 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 IPTi-ordered spaces, i=0,1,2, in the part II the axioms IPTi-ordered spaces, i=3,4,5 and IPRj-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 examples are given to illustrate the concepts. Moreover, some important results related to these separations have been obtained