Geodesic
Monotone path-connectedness of Chebyshev sets in the space~$C(Q)$
Sbornik. Mathematics, Tome 197 (2006) no. 9, pp. 1259-1272

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The structure of Chebyshev sets and strict suns in the space $C(Q)$ with compact $Q$ is considered. It is shown that a boundedly compact strict sun in $C(Q)$ (in particular, a bounded compact Chebyshev set) is monotone path-connected and in particular, $P$-acyclic. It is demonstrated that a monotone path-connected Chebyshev set in $C(Q)$ is a sun. Bibliography: 25 titles. 
@article{SM_2006_197_9_a0,
     author = {A. R. Alimov},
     title = {Monotone path-connectedness of {Chebyshev} sets in the space~$C(Q)$},
     journal = {Sbornik. Mathematics},
     pages = {1259--1272},
     publisher = {mathdoc},
     volume = {197},
     number = {9},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_9_a0/}
}
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A. R. Alimov. Monotone path-connectedness of Chebyshev sets in the space~$C(Q)$. Sbornik. Mathematics, Tome 197 (2006) no. 9, pp. 1259-1272. http://geodesic.mathdoc.fr/item/SM_2006_197_9_a0/