This article is cited in 10 papers

Topology of the hyperspace of convex bodies of constant width

L. E. Bazilevich

Lviv Polytechnic National University

Abstract: 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.

UDC: 515.12

Received: 14.04.1995

DOI: 10.4213/mzm1670

 English version: Mathematical Notes, 1997, 62:6, 683–687

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