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

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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/}
}
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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/