On asymptotic dimension and a property of Nagata

2008/12/09 by Higes, J., Mitrra, A.
#18B30 #20H15 (Secondary) #54C55 (Primary) #54E35 #54F45 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.0812.1641

Abstract

In this note we prove that every metric space (X, d) of asymptotic dimmension at most n is coarsely equivalent to a metric space (Y, D) that satisfies the following property of Nagata: For every n+2 points y₁,..., y_n+2 in Y and for every x in Y there exist two different i,j such that D(y_i,y_j)≤ D(x,y_i). This solves problem 1400 of the book Open problems in Topology II.

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