Geodesic
The connectivity and approximative properties of sets in linear normed spaces
Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 193-204

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The connectivity of suns is investigated. It is shown that a sun is connected in finite-dimensional space. A set $M$ in uniformly convex space $X$ is shown to be approximatively compact if and only if $M$ is $P$-compact and the metric projection of $X$ onto $M$ is upper semicontinuous. 
@article{MZM_1975_17_2_a2,
     author = {V. A. Koshcheev},
     title = {The connectivity and approximative properties of sets in linear normed spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {193--204},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a2/}
}
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V. A. Koshcheev. The connectivity and approximative properties of sets in linear normed spaces. Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 193-204. http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a2/