We introduce the notion of a semi-I-regular set and investigate some of its properties. We show that it is weaker than the notion of a regular-I-closed set. Additionally, we also introduce the notion of an ABI -set by using the semi-I-regular set and study some of its properties. We conclude that a subset A of an ideal topological space (X,τ,I) is open if and only if it is an ABI -set and a pre-I-open set.
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.
First, we introduce the notion of fI-sets and investigate their properties in ideal topological spaces. Then, we also introduce the notions of RIC-continuous, fI-continuous and contra*-continuous functions and we show that a function f: (X,τ,I) to (Y,ϕ) is RIC -continuous if and only if it is fI-continuous and contra*-continuous.
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.
In 1986, Tong  proved that a function f : (X,τ)→(Y,ϕ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, AI-sets and AI -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, ϕ) is continuous if and only if it is α-I-continuous and AI-continuous.
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
The applicability of a new leaching method, the HSS (H2O2-Na2SO4-H2SO4) system, in the extraction of uranium from Saricaolu-Bergama Region low grade ore, and the efficiency of Acigol Lake (Denizli)-Turkey water as a natural source of Na2SO4 has been investigated. The effect of H2SO4 concentration, temperature, leaching time, H2O2 and Na2SO4 concentrations and the amount of Acigol Lake water on the extraction of uranium was examined. HSS was found suitable for the extraction of uranium from Saricaolu-Bergama Region samples and it was observed that the acid consumption could be decreased by adding Na2SO4.