Geodesic
On convex closed bounded bodies without farthest points such that the closure of their complement is antiproximinal
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 98-104

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A bounded closed convex Chebyshev approximative compact body $M\subset X=L_1[0,1]$ without farthest points is constructed such that $\overline{X\setminus M}$ is antiproximinal.
Mots-clés : antiproximinal set
Keywords: farthest points. 
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     author = {V. S. Balaganskii},
     title = {On convex closed bounded bodies without farthest points such that the closure of their complement is antiproximinal},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {98--104},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a11/}
}
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V. S. Balaganskii. On convex closed bounded bodies without farthest points such that the closure of their complement is antiproximinal. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 98-104. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a11/