Geodesic
Sets in $\mathbb {R}^n$ monotone path-connected with respect to some norm
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 53-55 
E. A. Savinova. Sets in $\mathbb {R}^n$ monotone path-connected with respect to some norm. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 53-55. http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a8/
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     title = {Sets in $\mathbb {R}^n$ monotone path-connected with respect to some norm},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions on a path-connected set $M$ in $\mathbb {R}^n$ that are necessary and sufficient for $M$ to be monotone path-connected with respect to some norm are obtained.

[1] Alimov A.R., “Svyaznost solnts v prostranstve $c_0$”, Izv. RAN. Ser. matem., 69:4 (2005), 3–18

[2] Tsarkov I.G., “Svoistva monotonno lineino svyaznykh mnozhestv”, Izv. RAN. Ser. matem., 85:2 (2021), 142–171

[3] Alimov A.R., “Monotone path-connectedness of strict suns”, Lobachevskii J. Math., 43:3 (2022), 519–527

[4] Brosowski B., Deutsch F., Lambert J., Morris P.D., “Chebyshev sets which are not suns”, Math. Ann., 212:2 (1974), 89–101

[5] Shklyaev K.S., “Ploskie mnozhestva, chebyshevskie v kakoi-libo norme”, Vestn. Mosk. un-ta. Matem. Mekhan., 2021, no. 2, 35–39

[6] Alimov A.R., Tsarkov I.G., “Svyaznost i solnechnost v zadachakh nailuchshego i pochti nailuchshego priblizheniya”, Uspekhi matem. nauk, 71:1(427) (2016), 3–84