Good metric spaces without good parameterizations

@article{Semmes1996GoodMS,
  title={Good metric spaces without good parameterizations},
  author={S. Semmes},
  journal={Revista Matematica Iberoamericana},
  year={1996},
  volume={12},
  pages={187-275}
}
  • S. Semmes
  • Published 30 April 1996
  • Mathematics
  • Revista Matematica Iberoamericana
A classical problem in geometric topology is to recognize when a topological space is a topological manifold. This paper addresses the question of when a metric space admits a quasisymmetric parametrization by providing examples of spaces with many Eucledian-like properties which are nonetheless substantially different from Euclidean geometry. These examples are geometrically self-similar versions of classical topologically self-similar examples from geometric topology, and they can be realized… 
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