The hyperspace of the closed unit interval is a Hilbert cube
| Autor: | J. E. West, R. M. Schori |
|---|---|
| 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 |
| Externí odkaz: |
|