It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
@article{bwmeta1.element.bwnjournal-article-fmv156i1p67bwm,
author = {W. Kirk},
title = {Hyperconvexity of $\mathbb{R}$-trees},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {67-72},
zbl = {0913.54030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv156i1p67bwm}
}
Kirk, W. Hyperconvexity of ℝ-trees. Fundamenta Mathematicae, Tome 158 (1998) pp. 67-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv156i1p67bwm/
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