Non-positive curvature and the Ptolemy inequality

Details Non-positive curvature and the Ptolemy inequality Non-positive curvature and the Ptolemy inequality

2007-05-08

arxiv.org/abs/0705.1042v1

Mathematics

Metric Geometry

11 pages, 2 figures

Scientific paper

We provide examples of non-locally compact geodesic Ptolemy metric spaces
which are not uniquely geodesic. On the other hand, we show that locally
compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we
prove that a metric space is CAT(0) if and only if it is Busemann convex and
Ptolemy.

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