Generalized oscillations for generalized continuities

Year, pages: 2011, 119 - 125

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

Borsík, J. 2011. Generalized oscillations for generalized continuities. In Tatra Mountains Mathematical Publications, vol. 49, no.2, pp. 119-125. 1210-3195.

Borsík, J. (2011). Generalized oscillations for generalized continuities. Tatra Mountains Mathematical Publications, 49(2), 119-125. 1210-3195.