Uniformly disconnected space

In mathematics, a uniformly disconnected space is a metric space (X,d) for which there exists λ>0 such that no pair of distinct points x,y∈X can be connected by a λ-chain. A λ-chain between x and y is a sequence of points x=x0,x1,…,xn=y in X such that d(xi,xi+1)≤λd(x,y),∀i∈{0,…,n}.[1]

## Properties

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

## References

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" (in en). Analysis and Geometry in Metric Spaces 5 (1): 69–77. doi:10.1515/agms-2017-0004. ISSN 2299-3274. https://www.degruyter.com/document/doi/10.1515/agms-2017-0004/html.

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