Geodesic
Alexandroff's Double Arrow Compact Space and Approximation Theory
Matematičeskie zametki, Tome 69 (2001) no. 6, pp. 820-827.

Voir la notice de l'article provenant de la source Math-Net.Ru

A compact space $\widetilde Q$ similar to the compact space known as Alexandroff's double arrow space is constructed. It is shown that the real space $C(\widetilde Q)$ has no Chebyshev subspaces of codimension $>1$, but the complex space $C(\widetilde Q)$ has such subspaces. 
@article{MZM_2001_69_6_a1,
     author = {L. P. Vlasov},
     title = {Alexandroff's {Double} {Arrow} {Compact} {Space} and {Approximation} {Theory}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {820--827},
     publisher = {mathdoc},
     volume = {69},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a1/}
}
TY  - JOUR
AU  - L. P. Vlasov
TI  - Alexandroff's Double Arrow Compact Space and Approximation Theory
JO  - Matematičeskie zametki
PY  - 2001
SP  - 820
EP  - 827
VL  - 69
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a1/
LA  - ru
ID  - MZM_2001_69_6_a1
ER  - 
%0 Journal Article
%A L. P. Vlasov
%T Alexandroff's Double Arrow Compact Space and Approximation Theory
%J Matematičeskie zametki
%D 2001
%P 820-827
%V 69
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a1/
%G ru
%F MZM_2001_69_6_a1
L. P. Vlasov. Alexandroff's Double Arrow Compact Space and Approximation Theory. Matematičeskie zametki, Tome 69 (2001) no. 6, pp. 820-827. http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a1/

[1] Phelps R. R., “C̆ebys̆ev subspaces of finite codimension in $C(X)$”, Pacific J. Math., 13:2 (1963), 647–655 | MR | Zbl

[2] Garkavi A. L., “Zadacha Khelli i nailuchshee priblizhenie v prostranstve nepreryvnykh funktsii”, Izv. AN SSSR. Ser. matem., 31:3 (1967), 641–656 | MR | Zbl

[3] Garkavi A. L., “O kompaktakh, dopuskayuschikh chebyshevskie sistemy mer”, Matem. sb., 74 (116):2 (1967), 209–217 | MR | Zbl

[4] Brown A. L., “Chebyshev subspaces of finite codimension in spaces of continuous functions”, J. Austral. Math. Soc. Ser. A, 26:1 (1978), 99–109 | DOI | MR | Zbl

[5] Vlasov L. P., “Approksimativnye svoistva podprostranstv konechnoi korazmernosti v $C(Q)$”, Matem. zametki, 28:2 (1980), 205–222 | MR | Zbl

[6] Vlasov L. P., “Suschestvovanie elementov nailuchshego priblizheniya v kompleksnom $C(Q)$”, Matem. zametki, 40:5 (1986), 627–634 | MR | Zbl

[7] Vlasov L. P., “Chebyshevskie podprostranstva konechnoi korazmernosti v kompleksnom $C(Q)$”, Matem. zametki, 62:2 (1997), 178–191 | MR | Zbl

[8] Danford N., Shvarts Dzh., Lineinye operatory. Obschaya teoriya, IL, M., 1962

[9] Kelli Dzh. L., Obschaya topologiya, Nauka, M., 1968

[10] Fedorchuk V., “O bikompaktakh s nesovpadayuschimi razmernostyami”, Dokl. AN SSSR, 182:2 (1968), 275–277 | MR | Zbl