Relations approximated by continuous functions in the Vietoris topology
Relations approximated by continuous functions in the Vietoris topology
Let $X$ be a Tikhonov space, $C(X)$ be the space of all continuous real-valued functions defined on $X$, and ${\rm CL}(X \times {{\mathbb R}})$ be the hyperspace of all nonempty closed subsets of $X\times {{\mathbb R}}$. We prove the following result: Let