On convex bodies of constant width
By L. Bazylevych, M. Zarichnyi. 2004
110 citations recorded by the source corpus.
Abstract We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in R n is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of constant width as well as for the pairs of compact convex sets of constant relative width. Besides, it is proved that the projection map of compact closed subsets of constant width is not 0-soft in the sense of Shchepin, in particular, is not open.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d8a0d847a8a2b4c69a4f6b51b56ed911d6fa2491
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A quantitative program for Hadwiger’s covering conjecture (2009, background): “It is known in convexity (see [11]) that”