The concepts of I-R closed set, AI-R-set, αIM1-set, αIM2-set, αIN1-set, αIN2-set, αIN3-set, αIN4-set and αIN5-set are introduced via idealization. New decompositions of some weaker forms of continuity are obtained by using these sets.
We study the concepts of α-I-continuity and α-I-openness in ideal topological spaces, and obtain several characterizations and some properties of these functions. Also,
we investigate its relationship with other types of functions.
We introduce the notions of δ-I- open sets and semi δ-I-continuous functions in ideal topological spaces and investigate some of their properties. Additionally, we obtain decompositions
of semi-I-continuous functions and α-I-continuous functions by using δ-I-open sets.
The main purpose of this paper is to introduce *-operfect, τ*-clopen, α-*-closed, strongly α-*-closed and pre-*-closed sets. We compare them and obtain a diagram to show their relationships among these sets and related