Geodesic
Example of an antiproximinal, but not a 2-antiproximinal convex closed bounded body
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2016), pp. 49-52 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An example of an antiproximinal but not 2-antiproximinal convex closed bounded body is constructed in the space $\bf{c}_0$ endowed with Day's norm. 
@article{VMUMM_2016_5_a8,
     author = {B. B. Bednov},
     title = {Example of an antiproximinal, but not a 2-antiproximinal convex closed bounded body},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {49--52},
     year = {2016},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a8/}
}
TY  - JOUR
AU  - B. B. Bednov
TI  - Example of an antiproximinal, but not a 2-antiproximinal convex closed bounded body
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 49
EP  - 52
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a8/
LA  - ru
ID  - VMUMM_2016_5_a8
ER  - 
%0 Journal Article
%A B. B. Bednov
%T Example of an antiproximinal, but not a 2-antiproximinal convex closed bounded body
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 49-52
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a8/
%G ru
%F VMUMM_2016_5_a8
B. B. Bednov. Example of an antiproximinal, but not a 2-antiproximinal convex closed bounded body. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2016), pp. 49-52. http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a8/

[1] Bednov B.B., “Ob $n$-antiproksiminalnykh mnozhestvakh”, Vestn. Mosk. un-ta. Matem. Mekhan., 2015, no. 3, 29–34 | MR | Zbl

[2] Borodin P.A., “O vypuklosti $N$-chebyshevskikh mnozhestv”, Izv. RAN. Ser. matem., 75:5 (2011), 19–46 | DOI | MR | Zbl

[3] Day M.M., “Strict convexity and smoothness of normed spaces”, Trans. Amer. Math. Soc., 78:2 (1955), 516–528 | DOI | MR | Zbl

[4] Cobzaş S., “Multimifoarte neproximinale in $\bf{c}_0$”, Rev. anal. numer. şi teor. approxim., 2 (1973), 137–141 | MR

[5] Edelstein M., “Antiproximal sets”, J. Approx. Theory, 49 (1987), 252–255 | DOI | MR | Zbl

[6] Balaganskii V.S., “Ob antiproksiminalnykh vypuklykh ogranichennykh mnozhestvakh v prostranstve $\mathrm{ \bf \bf{c}_0}(\Gamma)$ s normoi Deya”, Matem. zametki, 79:3 (2006), 323–338 | DOI | MR | Zbl

[7] Edelstein M., Thompson A.C., “Some results on nearest points and support properties of convex sets in $\mathrm{ \bf \bf{c}_0}$”, Pacif. J. Math., 40:3 (1972), 553–560 | DOI | MR | Zbl

[8] Kobzash S., “Vypuklye antiproksiminalnye mnozhestva v prostranstvakh $\mathrm{ \bf \bf{c}_0}$ i $\mathrm{ \bf c}$”, Matem. zametki, 17:3 (1975), 449–457 | Zbl