Geodesic
A characterization of almost continuity and weak continuity
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 133-136

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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 $X$.
Classification : 54C08, 54C10
Keywords: almost continuous function; weakly continuous function 
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Petalas, Chrisostomos; Vidalis, Theodoros. A characterization of almost continuity and weak continuity. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 133-136. http://geodesic.mathdoc.fr/item/AUPO_2004__43_1_a12/