Keskin, A.Yuksel, S.2020-03-262020-03-2620060236-5294https://dx.doi.org/10.1007/s10474-006-0101-1https://hdl.handle.net/20.500.12395/20602We 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 AB(I) -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,tau,I) is open if and only if it is an AB(I) -set and a pre-I-open set.en10.1007/s10474-006-0101-1info:eu-repo/semantics/closedAccessAB(I)-setsemi-I-regular setdecomposition of continuitydecomposition of RIC-continuitydecomposition of A(I)-continuitytopological idealArticle1133227241Q2WOS:000241376900004Q3