Idealization of a decomposition theorem |
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Authors: | A. Keskin T. Noiri Ş Yüksel |
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Affiliation: | (1) Department of Mathematics, Selcuk University, 42031 Campus-Konya, Turkey;(2) Department of Mathematics, Yatsushiro College of Technology Yatsushiro, Kumamoto 866-8501, Japan |
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Abstract: | In 1986, Tong [13] 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, A I-sets and A I -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 A I-continuous. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | A-set regular-I-closed set regular closed set AI -set decomposition of continuity topological ideal |
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