Idealization of a decomposition theorem

Author： Keskin A.   Noiri T.   Yüksel Ş  

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.102, Iss.4, 2004-01, pp. : 269-278

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Abstract

In 1986, Tong [13] proved that a function f : (X,&tgr;)→(Y,φ) is continuous if and only if it is &agr;-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,&tgr;,I)→(Y, φ) is continuous if and only if it is &agr;-I-continuous and AI-continuous.

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