GENERALIZED OSCILLATIONS FOR GENERALIZED CONTINUITIES

Abstract

Let $(X,\fg)$ be a generalized topological space, $(Y,d)$ a metric one and $f:X\to Y$ a function. We can define a generalized oscillation of $f$ at $x\in X$ as $k_f^\fg(x)=\inf\{ \diam f(A):  A\in\fg, x\in A\}$. We discuss some properties of the generalized oscillation.