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24. 2. 2023.
SOME METRICAL AND TOPOLOGICAL PROPERTIES OF THE RIVER METRIC ON $\mathbb{R}^2$
In this paper we consider some metrical and topological properties of the river metric $d^*$ in the plane $\mathbb{R}^2^2$. We give the form of the metric segment and the set of all points that are equidistant from two points in $(\rR^2,d^*)$. We also give the characterization of a compact sets in this space.