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# hyperspace

Given a continuum with a metric , we let to denote the hyperspace of all nonempty closed subsets of equipped with the Hausdorff metric defined by

(see e.g. [Nadler 1978, (0.1), p. 1 and (0.12), p. 10]). If tends to zero as tends to infinity, we put . Further, we denote by the hyperspace of singletons of , and by the hyperspace of all subcontinua of , i.e., of all connected elements of . Since is homeomorphic to , there is a natural embedding of into , and so we can write . Thus one can consider a retraction from either or onto .

Next: indecomposable Up: Definitions Previous: HU-terminal
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30