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CHEBYSHEV SUBSETS OF A HILBERT SPACE SPHERE
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 107 / Issue 3 / December 2019
- Published online by Cambridge University Press:
- 21 November 2019, pp. 289-301
- Print publication:
- December 2019
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- Article
- Export citation
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The Chebyshev conjecture posits that Chebyshev subsets of a real Hilbert space
$X$ are convex. Works by Asplund, Ficken and Klee have uncovered an equivalent formulation of the Chebyshev conjecture in terms of uniquely remotal subsets of 
$X$. In this tradition, we develop another equivalent formulation in terms of Chebyshev subsets of the unit sphere of 
$X\times \mathbb{R}$. We characterise such sets in terms of the image under stereographic projection. Such sets have superior structure to Chebyshev sets and uniquely remotal sets.
