Geodesic
Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets
Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 919-931

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The sets with continuous selection from near-best approximations and the monotone path-connected sets are studied; several examples of such sets are also considered.
Keywords: continuous selections, monotone path-connected sets. 
@article{MZM_2017_101_6_a11,
     author = {I. G. Tsar'kov},
     title = {Continuous $\varepsilon${-Selection} and {Monotone} {Path-Connected} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {919--931},
     publisher = {mathdoc},
     volume = {101},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a11/}
}
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I. G. Tsar'kov. Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets. Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 919-931. http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a11/