Uniformly disconnected space

In mathematics, a uniformly disconnected space is a metric space $$(X,d)$$ for which there exists $$\lambda > 0$$ such that no pair of distinct points $$x,y \in X$$ can be connected by a $$\lambda$$-chain. A $$\lambda$$-chain between $$x$$ and $$y$$ is a sequence of points $$x= x_0, x_1, \ldots, x_n = y$$ in $$X$$ such that $$d(x_i,x_{i+1}) \leq \lambda d(x,y), \forall i \in \{0,\ldots,n\}$$.

Properties
Uniform disconnectedness is invariant under quasi-Möbius maps.