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.
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Keskin, A., Noiri, T. & Yüksel, Ş. Idealization of a decomposition theorem. Acta Mathematica Hungarica 102, 269–278 (2004). https://doi.org/10.1023/B:AMHU.0000024677.08811.6a
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DOI: https://doi.org/10.1023/B:AMHU.0000024677.08811.6a