Abstract
In a two-dimensional Banach space \(X\), the class of Chebyshev sets coincides with the class of closed and monotone path- connected sets if and only if \(X\) is strictly convex. In a finite-dimensional Banach space \(X\) of dimension at least \(3\), this coincidence occurs if and only if \(X\) is smooth and strictly convex.
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Acknowledgments
The author thanks P. A. Borodin for his attention to the work and useful remarks
Funding
This work was supported by the Russian Science Foundation under grant no. 22-21-00415.
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Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 483-493 https://doi.org/10.4213/mzm13314.
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Bednov, B.B. Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets. Math Notes 111, 505–514 (2022). https://doi.org/10.1134/S000143462203018X
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DOI: https://doi.org/10.1134/S000143462203018X