Geodesic
Chebyshev Sets in C[0,1] Which are not Suns
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 35-37

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Consider approximation of elements of C[0, 1] with respect to the sup-norm by a non-empty subset V of C[0, 1]. Of interest in recent years are subsets V called suns. As C[0, 1] is an MS-space [1, 5], the suns V of C[0, 1] are precisely those subsets V for which each local best approximation is a global best approximation. 
Dunham, Charles B. Chebyshev Sets in C[0,1] Which are not Suns. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 35-37. doi: 10.4153/CMB-1975-006-7
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     title = {Chebyshev {Sets} in {C[0,1]} {Which} are not {Suns}},
     journal = {Canadian mathematical bulletin},
     pages = {35--37},
     year = {1975},
     volume = {18},
     number = {1},
     doi = {10.4153/CMB-1975-006-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-006-7/}
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