Geodesic
Topology of the hyperspace of convex bodies of constant width
Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 813-819.

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The hyperspace of all convex bodies of constant width in Euclidean space $\mathbb R^n$, $n\ge2$, is proved to be homeomorphic to a contractible $Q$-manifold ($Q$ denotes the Hilbert cube). The proof makes use of an explicitly constructed retraction of the entire hyperspace of convex bodies on the hyperspace of convex bodies of constant width. 
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     title = {Topology of the hyperspace of convex bodies of constant width},
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L. E. Bazilevich. Topology of the hyperspace of convex bodies of constant width. Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 813-819. http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a1/

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