Geodesic
The concept of approximative compactness and alternate versions of it
Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 337-348 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study various characteristics and generalizations of approximative compact and approximative weak compact sets. We generalize a result of Asplund concerning sets whose intersection with each halfspace is an existence set. In particular, in smooth Efimov–Stechkin spaces, such a set, if it is a Chebyshev set, must be convex. 
@article{MZM_1974_16_2_a17,
     author = {L. P. Vlasov},
     title = {The concept of approximative compactness and alternate versions of it},
     journal = {Matemati\v{c}eskie zametki},
     pages = {337--348},
     year = {1974},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a17/}
}
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L. P. Vlasov. The concept of approximative compactness and alternate versions of it. Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 337-348. http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a17/