The cactus tree of a metric space

Papasoglu, Panos¹ ; Swenson, Eric²

¹Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, UK
²Mathematics Department, Brigham Young University, Provo UT 84602, USA

Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2547-2578

Résumé

We extend the cactus theorem of Dinitz, Karzanov, Lomonosov to metric spaces. In particular we show that if X is a separable continuum which is not separated by n − 1 points then the set of all n–tuples of points separating X can be encoded by an ℝ–tree.

Détail

DOI : 10.2140/agt.2011.11.2547

Keywords: pretree, cuts

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