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

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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. 
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     author = {E. A. Savinova},
     title = {Sets in $\mathbb {R}^n$ monotone path-connected with respect to some norm},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {53--55},
     publisher = {mathdoc},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a8/}
}
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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/