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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 6 > No. 1


On ^PI-Sets in Ideal Topological Spaces

PP: 97-103
Rodyna A. Hosny, A. M. Abd El-latif,
In this paper, we define and study the notions of pre-I -kernel for any set (briefly, ∧P I ( )), generalized ∧P I -sets, ∧P I -closed sets and I-generalized pre-closed (briefly, I -gp-closed) sets by using pre-I -open sets in ideal topological spaces. The family of ∧P I -sets, which is stronger than the class of pre-I -open sets, is introduced. The collection of ∧P I -sets is Alexandroff space is proven. Also, we propose and characterize some relevant low separation axioms, namely pre-I τ 1 and pre-I τ 1 2 . The concepts ∧P( ) (resp. ∧( ), ∧I ( )) from pre-I -kernel of any set with different kinds of ideals are deduced. Variants of continuity, namely ∧P I -continuous, quasi-∧P I -continuous, ∧P I -irresolute and strongly pre-I -irresolute functions in terms of ∧P I -open sets are characterized. Moreover, the relationships between these classes of functions are studied. Some properties and characterizations of them are obtained.

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