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Öğe Decompositions of I-Continuity and Continuity(2004) Keskin, A.; Yüksel, S.; Noırı, T.r1-açık küme ve m1 -açık küme kavramlarını tanımladık ve bu kümeleri kullanarak l-açık kümelerin ayrışımlarını elde ettik. Ayrıca, weakly I-lokal-kapalı küme kavramını tanımladık ve açık kümelerin ayrışımlarını elde ettik. Son olarak, I- sürekli ve sürekli fonksiyonların ayrışımlarını elde ettik.Öğe ON bD-SETS AND ASSOCIATED SEPARATION AXIOMS(SPRINGER SINGAPORE PTE LTD, 2009) Keskin, A.; Noiri, T.Here, first we introduce and investigate bD-sets by using the notion of b-open sets to obtain some weak separation axioms. Second, we introduce the notion of gb-closed sets and then investigate some relations of between b-closed and gb-closed sets. We also give a characterization of b-T-1/2 spaces via gb-closed sets. We introduce two new weak homeomorphisms which are important keys between General Topology and Algebra. Using the notion of m(X)-structures, we give a characterization theorem of m(X)-T-2 spaces. Finally, we give some examples related to the digital line.Öğe On semi-I-regular sets, AB(I)-sets and decompositions of continuity, RIC-continuity, A(I)-continuity(AKADEMIAI KIADO, 2006) Keskin, A.; Yuksel, S.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 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.Öğe Strong B I-sets and a Decomposition of Continuity via Idealization(2005) Keskin, A.; Noiri, T.; Yüksel, S.We introduce the notions of Q I-sets and strong B I-sets. Then we investigate properties of strong B I-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.