Alimov, Alexey R. On approximative properties of locally Chebyshev sets. (English) Zbl 1405.41017 Proc. Inst. Math. Mech., Natl. Acad. Sci. Azerb. 44, No. 1, 36-42 (2018). Summary: A locally Chebyshev set is a set whose intersection with some closed neighbourhood with center at any point of this set is a Chebyshev set. The paper is concerned with local and global approximative properties of sets. A number of new properties of locally Chebyshev sets and local strict suns are put forward. We give an elementary proof of the recent Flerov’s result to the effect that in a two-dimensional normed linear space a connected locally Chebyshev set is a Chebyshev set. Cited in 2 Documents MSC: 41A50 Best approximation, Chebyshev systems Keywords:Chebyshev set; locally Chebyshev set; local strict sun; best approximation; monotone path-connected set PDFBibTeX XMLCite \textit{A. R. Alimov}, Proc. Inst. Math. Mech., Natl. Acad. Sci. Azerb. 44, No. 1, 36--42 (2018; Zbl 1405.41017)