Uniformly disconnected space
A metric space (X, d) is called uniformly disconnected if there is a positive number λ such that no two distinct points x and y in X can be connected by a λ-chain. A λ-chain from x to y is a finite sequence x = x0, x1, ..., xn = y in X where each step is not longer than λ times the distance between x and y: d(xi, xi+1) ≤ λ d(x, y) for every i.
Put simply, with such a λ fixed, you cannot travel from x to y by a chain of small steps that are all controlled by the overall distance between x and y. This property stays true under a broad class of transformations known as quasi-Möbius maps.
This page was last edited on 2 February 2026, at 16:59 (CET).