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 $x=x_0,x_1,\dots ,x_n=y$ in $X$ such that $d(x_i,x_{i+1})\le \lambda d(x,y),\mathrm{\forall }i\in \{0,\dots ,n\}$.

Properties

Uniform disconnectedness is invariant under quasi-Möbius maps.

References

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