Abstract
Let X X be a Tychonoff space, let C ( X ) C(X) be the space of all continuous real-valued functions defined on X X and let C L ( X × R ) CL(X \times R) be the hyperspace of all nonempty closed subsets of X × R X\times R . We prove the following result. Let X X be a locally connected, countably paracompact, normal q q -space without isolated points, and let F ∈ C L ( X × R ) F \in CL(X \times R) . Then F F is in the closure of C ( X ) C(X) in C L ( X × R ) CL(X \times R) with the locally finite topology if and only if F F is the graph of a cusco map. Some results concerning an approximation in the Vietoris topology are also given.
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