Convexity of Chebyshev sets with respect to tangent directions

2018 ◽  
Vol 73 (2) ◽  
pp. 366-368 ◽  
Author(s):  
A. R. Alimov ◽  
E. V. Shchepin
Keyword(s):  
Chebyshev Sets

scholarly journals Examples of Chebyshev Sets in Matrix Spaces

1999 ◽  
Vol 99 (1) ◽  
pp. 44-53 ◽  
Author(s):  
A.R Alimov ◽  
H Berens
Keyword(s):  
Chebyshev Sets ◽  
Matrix Spaces

scholarly journals On the distance between two Chebyshev sets in Banach spaces

1997 ◽  
Vol 20 (3) ◽  
pp. 611-612
Author(s):  
Wagdy G. El-Sayed
Keyword(s):  
Banach Spaces ◽  
Chebyshev Sets

The paper answers a question concerning the distance between two Chebyshev sets in some Banach spaces.

Chebyshev sets and approximately convex sets

1967 ◽  
Vol 2 (2) ◽  
pp. 600-605 ◽  
Author(s):  
L. P. Vlasov
Keyword(s):  
Convex Sets ◽  
Chebyshev Sets

Dispersed Chebyshev sets and coverings by balls

1981 ◽  
Vol 257 (2) ◽  
pp. 251-260 ◽  
Author(s):  
Victor Klee
Keyword(s):  
Chebyshev Sets

Approximation properties of sets with bounded complements

1981 ◽  
Vol 89 (1-2) ◽  
pp. 75-86 ◽  
Author(s):  
C. Franchetti ◽  
P. L. Papini
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Metric Projection ◽  
Special Role ◽  
Approximation Properties ◽  
Chebyshev Sets

SynopsisGiven a Banach space X, we investigate the behaviour of the metric projection PF onto a subset F with a bounded complement.We highlight the special role of points at which d(x, F) attains a maximum. In particular, we consider the case of X as a Hilbert space: this case is related to the famous problem of the convexity of Chebyshev sets.

CHEBYSHEV SUBSETS OF A HILBERT SPACE SPHERE

2019 ◽  
Vol 107 (3) ◽  
pp. 289-301
Author(s):  
THEO BENDIT
Keyword(s):  
Hilbert Space ◽  
Unit Sphere ◽  
Stereographic Projection ◽  
Real Hilbert Space ◽  
Equivalent Formulation ◽  
Chebyshev Sets

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.

Sign in / Sign up

Export Citation Format

Share Document