Geodesic
Chebyshev subspaces of vector-valued functions
Matematičeskie zametki, Tome 19 (1976) no. 3, pp. 347-352

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

It is shown that if on a compact space $Q$ any polynomial $P_N(z)=\sum_1^Na_i\begin{pmatrix}f_{i1}\\\vdots\\f_{is}\end{pmatrix}$, $\sum_1^N|a_i|^2>0$, in a system of continuous vector functions with real coefficients such that $N=n\cdot s$ and $s=2p+1$ has at most $n-1$ zeros, then $Q$ is homeomorphic to a circle or a part of one. 
@article{MZM_1976_19_3_a3,
     author = {\`E. N. Morozov},
     title = {Chebyshev subspaces of vector-valued functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {347--352},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_3_a3/}
}
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È. N. Morozov. Chebyshev subspaces of vector-valued functions. Matematičeskie zametki, Tome 19 (1976) no. 3, pp. 347-352. http://geodesic.mathdoc.fr/item/MZM_1976_19_3_a3/