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 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.
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.
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