Boundedness of pretangent spaces to general metric spaces

@article{Bilet2012BoundednessOP,
  title={Boundedness of pretangent spaces to general metric spaces},
  author={Viktoriia Bilet and Oleksiy Dovgoshey},
  journal={arXiv: Metric Geometry},
  year={2012}
}
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,\infty) and prove that the distance set {d(x,p): x\in X} is w-strongly porous at 0 if and only if every pretangent space to X at p is bounded. 
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