Uniformly disconnected space explained

(X,d) for which there exists λ > 0 such that no pair of distinct points x,y \in X can be connected by a λ -chain.A λ -chain between x and y is a sequence of pointsx = x _{0,} x _{1,} \ldots, x _{n} = y in X such that d(x _{i,x} _{i+1} ) \leq λ d(x,y), \forall i \in \{ 0 ,\ldots,n\} .^[1]

Properties

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

References

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