E. A. Savinova, “Sets in <nobr>$\mathbb {R}^n$</nobr> monotone path-connected with respect to some norm”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, Number 1,Pages <nobr>53

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Short notes

Sets in $\mathbb {R}^n$ monotone path-connected with respect to some norm

E. A. Savinova^ab

^a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Moscow Center for Fundamental and Applied Mathematics

Abstract: 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.

Key words: monotone path-connectedness, $m$-connectedness, normed space.

UDC: 517.982.256

Received: 04.02.2022

DOI: 10.55959/MSU0579-9368-1-2023-1-53-55