Boundedness of pretangent spaces to general metric spaces

2012/10/02 by Bilet, Viktoriia, Dovgoshey, Oleksiy
#28A10 #54E35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1210.0656

Abstract

Let (X,d,p) be a metric space with a metric d and a marked point p. We define the set of w-strongly porous at 0 subsets of [0,∞) and prove that the distance set d(x,p): x∈ X is w-strongly porous at 0 if and only if every pretangent space to X at p is bounded.

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