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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.)
##### Keywords:
almost continuous function; weakly continuous function
Full Text:
##### References:
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