The hyperspace of the closed unit interval is a Hilbert cube

Schori, R. M.; West, J. E.

doi:10.1090/S0002-9947-1975-0390993-3

The hyperspace of the closed unit interval is a Hilbert cube
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by R. M. Schori and J. E. West PDF

Trans. Amer. Math. Soc. 213 (1975), 217-235 Request permission

Abstract:

Let X be a compact metric space and let ${2^X}$ 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 ${2^I}$ is homeomorphic to the Hilbert cube ${I^\infty }$, 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.

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Sur la contractilité des hyperspaces des continus localement convexes

30

Retractes absolus et hyperspaces des continus

32

Seminar on combinatorial topology