Algebraic & Geometric Topology 11 (2011) 2547–2578

DOI: 10.2140/agt.2011.11.2547

Abstract

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.

Keywords

pretree, cuts

Mathematical Subject Classification

Primary: 20E08, 54F15

Secondary: 05C40, 20F65, 54F05

References

Publication

Received: 1 September 2010
Revised: 23 January 2011
Accepted: 14 April 2011
Published: 13 September 2011

Authors