The hyperspace of the closed unit interval is a Hilbert cube
Autor: | J. E. West, R. M. Schori |
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Rok vydání: | 1975 |
Předmět: | |
Zdroj: | Transactions of the American Mathematical Society. 213:217-235 |
ISSN: | 1088-6850 0002-9947 |
Popis: | Let X be a compact metric space and let 2 X {2^X} be the space of all nonvoid closed subsets of X topologized with the Hausdorff metric. For the closed unit interval I the authors prove that 2 I {2^I} is homeomorphic to the Hilbert cube I ∞ {I^\infty } , settling a conjecture of Wojdyslawski that was posed in 1938. The proof utilizes inverse limits and near-homeomorphisms, and uses (and developes) several techniques and theorems in infinite-dimensional topology. |
Databáze: | OpenAIRE |
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