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A characterization of almost continuity and weak continuity. (English) Zbl 1064.54025
Summary: It is well known that a function \(f\) from a space \(X\) into a space \(Y\) is continuous if and only if, for every set \(K\) in \(X\) the image of the closure of \(K\) under \(f\) is a subset of the closure of the image of it.
In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets \(K\) of \(X\).
MSC:
54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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References:
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