A Hilbert space limit for the iterated hyperspace functor
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- by H. Toruńczyk and J. West PDF
- Proc. Amer. Math. Soc. 89 (1983), 329-335 Request permission
Abstract:
Let $X$ be a nondegenerate metric Peano continuum and let $P(X)$ be the hyperspace of closed, nonvoid subsets of $X$ equipped with the Hausdorff metric. Then the inclusion of $X$ into $P(X)$ as the single element sets is an isometry and we have a direct system $X \to P(X) \to P(P(X)) \to \cdots$ of isometric inclusions. Let $X’$ be the metric direct limit and ${X^*}$ be its completion. We prove that the pair $({X^*},X’)$ is homeomorphic to the pair $({l^2},l_\sigma ^2)$, where $l_\sigma ^2$ is the linear span in ${l^2}$ of the Hilbert cube.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 329-335
- MSC: Primary 54B20; Secondary 57N20
- DOI: https://doi.org/10.1090/S0002-9939-1983-0712646-1
- MathSciNet review: 712646