Almost continuous real functions

Abstract:

A blocking set of a function f is a closed set which does not intersect f but which intersects each continuous function with domain the same as f. It is shown that for each function which is not almost continuous, there exists a minimal blocking set. Using this property it is shown that there exists an almost continuous function with domain [0, 1] which is a ${G_\delta }$ set but is not of Baire Class 1, and that there exists an almost continuous function dense in the unit square.