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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)].
##### MSC:
 54C35 Function spaces in general topology 54E40 Special maps on metric spaces 54B20 Hyperspaces in general topology