Uniformly disconnected space Source: en.wikipedia.org/wiki/Uniformly_disconnected_space

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

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

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