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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 \(X\).
54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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