Abstract:Let $X$ be a locally connected, $b$-compact metric space and $E$ a closed subset of $X$. Let ${\Bbb G}$ be the space of all continuous real-valued functions defined on some closed subsets of $E$. We prove the equivalence of the ${\tau _{_{a\!w}}}$ and ${\tau ^c_{_{\!K}}}$ topologies on ${\Bbb G}$, where ${\tau _{_{a\!w}}}$ is the so called {Attouch-Wets} topology, defined in terms of uniform convergence of distance functionals, and ${\tau ^c_{_{\!K}}}$ is the topology of Kuratowski convergence on compacta.
Keywords: function spaces, Kuratowski convergence, hyperspaces
AMS Subject Classification: 54C35, 54C99