I-ω^*-Continuous and I-ω^*- Open Functions
Ideal topological space
I-ω^*-open set
ω-continuous function
I-ω^*-continuous function
I-ω^*-open function
In ideal topological space, we define and study a new class of functions known as I-ω^*-continuous functions by using I-ω^*-open sets. This idea is stronger than each of the classes (ω-continuous, ωb-continous, α-I_ω-continuous, pre-I_ω-continuous, β-I_ω-continuous, faintly- ω-continuous, slightly- ω-continuous, 〖 I〗_ω-c-continuous). Furthermore, relationships between this class and other relevant classes of functions are investigated, and some characterizations of this new class of functions are studied. Finally, we introduce the I-ω^*- open function as an extension of the ω- open function through I-ω^*-open sets, and some results are provided.