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A characterization of almost continuity and weak continuity

Chrisostomos Petalas; Theodoros Vidalis — 2004

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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 $X$ .

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