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arXiv · 0906.1916

On Ptolemaic metric simplicial complexes

S. M. Buckley·J. McDougall·D. J. Wraith
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Abstract

We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy's inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isometric to Euclidean space in terms of metric inversions.

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S. M. Buckley, J. McDougall, D. J. Wraith. 2009-06-10. On Ptolemaic metric simplicial complexes. https://doi.org/10.1017/s0305004110000125

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