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arXiv · 1506.05982

Tight Span of Subsets of The Plane With The Maximum Metric

Mehmet Kiliç·Şahin Koçak
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Abstract

We prove that a nonempty closed and geodesically convex subset of the $l_{\infty}$ plane $\mathbb{R}^2_{\infty}$ is hyperconvex and we characterize the tight spans of arbitrary subsets of $\mathbb{R}^2_{\infty}$ via this property: Given any nonempty $X\subseteq\mathbb{R}^2_{\infty}$, a closed, geodesically convex and minimal subset $Y\subseteq\mathbb{R}^2_{\infty}$ containing $X$ is isometric to the tight span $T(X)$ of $X$.

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Mehmet Kiliç, Şahin Koçak. 2015-06-19. Tight Span of Subsets of The Plane With The Maximum Metric. https://arxiv.org/abs/1506.05982

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