# Hyperconvexity of ℝ-trees

Fundamenta Mathematicae (1998)

- Volume: 156, Issue: 1, page 67-72
- ISSN: 0016-2736

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topKirk, W.. "Hyperconvexity of ℝ-trees." Fundamenta Mathematicae 156.1 (1998): 67-72. <http://eudml.org/doc/212261>.

@article{Kirk1998,

abstract = {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.},

author = {Kirk, W.},

journal = {Fundamenta Mathematicae},

keywords = {hyperconvex metric space; ℝ-tree; fixed point; nonexpansive mapping; complete -tree},

language = {eng},

number = {1},

pages = {67-72},

title = {Hyperconvexity of ℝ-trees},

url = {http://eudml.org/doc/212261},

volume = {156},

year = {1998},

}

TY - JOUR

AU - Kirk, W.

TI - Hyperconvexity of ℝ-trees

JO - Fundamenta Mathematicae

PY - 1998

VL - 156

IS - 1

SP - 67

EP - 72

AB - 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.

LA - eng

KW - hyperconvex metric space; ℝ-tree; fixed point; nonexpansive mapping; complete -tree

UR - http://eudml.org/doc/212261

ER -

## References

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- [13] F. Rimlinger, Free actions on ℝ-trees, Trans. Amer. Math. Soc. 332 (1992), 313-329. Zbl0803.20017
- [14] R. Sine, On nonlinear contractions in sup norm spaces, Nonlinear Anal. 3 (1979), 885-890. Zbl0423.47035
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- [16] F. Sullivan, Ordering and completeness of metric spaces, Nieuw Arch. Wisk. (3) 29 (1981), 178-193. Zbl0484.54024
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