2010/10/20 by Norbert Sauer, Sauer, Norbert · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Fixed Point Theorems Analysis #math.CO #math.DS #math.FA
paper · pdf · doi:10.48550/arxiv.1010.4212
arxiv created 2010/11/30 · arxiv updated 2010/12/01
A metric space M=(M,\de) is \em indivisible if for every colouring χ: M→ 2 there exists i∈ 2 and a copy N=(N, \de) of M in M so that χ(x)=i for all x∈ N. The metric space M is \em homogeneus if for every isometry α of a finite subspace of M to a subspace of M there exists an isometry of M onto M extending α. A homogeneous metric space U with set of distances D is an Urysohn metric space if every finite metric space with set of distances a subset of D has an isometry into U. The main result of this paper states that all countable Urysohn metric spaces with a finite set of distances are indivisible.