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Öğe Asp-sets and some weak separation axioms(AKADEMIAI KIADO, 2004) Noiri, T; Hatir, EWe shall introduce the notions of Lambdasp-closed and spg-closed sets. We also investigate properties of these sets and introduce some related new separation axioms.Öğe f(I)-sets and decomposition of RIC-continuity(AKADEMIAI KIADO, 2004) Keskin, A; Noiri, T; Yuksel, SFirst, we introduce the notion of f(I)-sets and investigate their properties in ideal topological spaces. Then, we also introduce the notions of R-I C-continuous, f(I)-continuous and contra*-continuous functions and we show that a function f : (X,tau,I) --> (Y, phi) is RIC-continuous if and only if it is f(I)-continuous and contra*-continuous.Öğe Idealization of a decomposition theorem(AKADEMIAI KIADO, 2004) Keskin, A; Noiri, T; Yuksel, SIn 1986, Tong [13] proved that a function f : (X, tau) --> (Y, phi) is continuous if and only if it is alpha-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A(I)-sets and A(I)-continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X, 7, 1) --> (Y, phi) is continuous if and only if it is alpha-I-continuous and A(I)-continuous.Öğe A note on f(I)-sets and f(I)-continuous functions(AKADEMIAI KIADO, 2005) Keskin, A; Noiri, T; Yuksel, SIn [6], we introduced and investigated the notions of f(I)-sets and f(I)-continuous functions in ideal topological spaces. In this paper, we investigate their further important properties.Öğe A note on strong beta-I-sets and strongly beta-I-continuous functions(AKADEMIAI KIADO, 2005) Hatir, E; Keskin, A; Noiri, TIn [6], we introduced and investigated the notions of strong,beta-I-open sets and strong beta-I-continuous functions in ideal topological spaces. In this paper, we investigate further their important properties.Öğe On semi-I-open sets and semi-I-continuous functions(AKADEMIAI KIADO, 2005) Hatir, E; Noiri, TWe investigate further properties of semi-I-open sets and semi-I-continuous functions introduced in [4] and give the notions of semi-I-open and semi-I-closed functions.Öğe Strong B-I-sets and a decomposition of continuity via idealization(AKADEMIAI KIADO, 2005) Keskin, A; Noiri, T; Yuksel, SWe introduce the notions of Q(I)-sets and strong B-I-sets. Then we investigate properties of strong BI-sets. Additionally, we obtain a new decomposition of continuity via idealization by using strong B-I-sets. Consequently, we extend a decomposition theorem of Dontchev [5] in terms of ideals.Öğe Strongly precontinuous functions(AKADEMIAI KIADO, 2005) Beceren, Y; Noiri, TRecall twelve classes of functions: strongly beta-irresolute [21], beta-irresolute [17], strongly semi-continuous [2], strongly alpha-continuous [3], almost irresolute [9], strongly alpha-irresolute [15], alpha-irresolute [16], alpha-precontinuous [5], almost alpha-irresolute [4], alpha-continuous [20], precontinuous [18] and beta-continuous [1] functions in topological spaces. Recently, Beceren and Noiri [7] introduced the concepts of strongly alpha-preirresolute and strongly beta-preirresolute functions. The purpose of the present paper is to introduce and investigate the notion of a new class of functions, namely strongly precontinuous functions, and give several characterizations and their properties. Relations between this type of functions and other classes of functions are obtained. The new class of strongly precontinuous functions, which is stronger than alpha-precontinuous functions [5], is a generalization of strongly alpha-continuous functions [3].Öğe Weakly pre-I-open sets and decomposition of continuity(AKADEMIAI KIADO, 2005) Hatir, E; Noiri, TWe introduce and investigate the notions of weakly pre-I-open sets and weakly pre-I-continuous functions. By using the results, he following decomposition is provided: a function f : (X, tau, 1) -> (Y, sigma) is continuous if and only if f is weakly pre-I-continuous and strongly B-1-continuous.