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Abstract  

Let X be a topological space and (Y,d) be a metric space. If f: XY is a function then there is a function a f : X → [0, ∞] such that f is almost continuous at x if and only if a f (x) = 0. Some properties of this function are investigated.

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Abstract  

The concepts of I-R closed set, A I-R-set, α I M 1-set, α I M 2-set, α I N 1-set, α I N 2-set, α I N 3-set, α I N 4-set and α I N 5-set are introduced via idealization. New decompositions of some weaker forms of continuity are obtained by using these sets.

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