On almost continuous functions (Q909286)

A function f: \(X\to Y\) is called almost continuous if for every open neighbourhood V of f(x), there is an open neighborhood U of x such that f(U) is contained in the interior of the closure of V. Several characterizations of this condition are proved. The author also proves some results on the relationship between almost continuity and a variety of conditions which are weaker than continuity or openness of a function.