Abstract: | The hyperspace of all convex bodies of constant width in Euclidean spaceR
n
,n≥2, is proved to be homeomorphic to a contractibleQ-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.
Translated fromMaternaticheskie Zametki, Vol. 62, No. 6, pp. 813–819, December, 1997
Translated by V. N. Dubrovsky |