Ascoli-type theorems for locally bounded quasicontinuous functions, minimal usco and minimal cusco maps

Abstract

Let $X$ be a locally compact space and let $(Y,d)$ be a nontrivial metric space such that $d$ has the Heine--Borel property. We prove Ascoli-type theorem for locally bounded quasicontinuous functions from $X$ to $Y$. Using the above result we also prove an Ascoli-type theorems for the spaces of minimal usco and minimal cusco maps from $X$ to $\Bbb R$.