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IP-Separation Axioms in Ideal Bitopological Ordered Spaces I |
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PP: 11-15 |
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Author(s) |
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A. Kandil,
O. Tantawy,
S. A. El-Sheikh,
M. Hosny,
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Abstract |
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| The aim of this paper is to use the concept of ideal I to study ideal bitopological ordered spaces (X,t1,t2,R,
I). Clearly, if
I = {f }, then every ideal bitopological ordered spaces are bitopological ordered spaces. In addition, if I = {f } and R is the equality
relation ”D ”, then every ideal bitopological ordered spaces are bitopological spaces. Therefore, these spaces are generalization of the
bitopological ordered spaces and bitopological spaces. In this and a subsequent paper, we use the notion of I-increasing (decreasing)
sets which based on the ideal I, to introduce separation axioms in ideal bitopological ordered spaces. Whereas this paper is devoted
to the axioms IPTi, (i = 0,1,2) in part II the axioms IPTi, (i = 3,4,5) and IPRj-ordered spaces, j = 0,1,2,3,4 are introduced and
studied. Some important results related these separations have obtained and the relationship between these axioms and the previous one
has been given. |
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