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

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

0.00 (0 votes) Original source: https://en.wikipedia.org/wiki/Uniformly disconnected space. Read more