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Kuratowski convergence on compact sets. (English) Zbl 0770.54016
Let \(X\) be a metric space and \(F\) the space of all continuous functions on closed subsets of \(X\) to \(\mathbb{R}^ m\). Identifying each \(f\in F\) with its graph as a subset of \(X\times\mathbb{R}^ m\) [the reviewer, Trans. Am. Math. Soc. 123, 267-272 (1966; Zbl 0151.297)] the author considers Kuratowski convergence on compact sets. The topology on subsets of \(F\) is derived from a related hyperspace topology. For a related work see L. Holá [Bull. Aust. Math. Soc. 44, 11-18 (1991; Zbl 0716.54013)].
54C35 Function spaces in general topology
54E40 Special maps on metric spaces
54B20 Hyperspaces in general topology