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Uniformly disconnected space

From Wikipedia, the free encyclopedia

In mathematics, a uniformly disconnected space is a metric space for which there exists such that no pair of distinct points can be connected by a -chain. A -chain between and is a sequence of points in such that .[1]

Properties

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Uniform disconnectedness is invariant under quasi-Möbius maps.[2]

References

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  1. ^ Heinonen, Juha (2001). Lectures on Analysis on Metric Spaces. Universitext. New York: Springer-Verlag. pp. x+140. ISBN 0-387-95104-0.
  2. ^ Heer, Loreno (2017-08-28). "Some Invariant Properties of Quasi-Möbius Maps". Analysis and Geometry in Metric Spaces. 5 (1): 69–77. arXiv:1603.07521. doi:10.1515/agms-2017-0004. ISSN 2299-3274.