# characterization of connected compact metric spaces.

Let $(A,d)$ be a compact metric space. Then $A$ is connected $\Longleftrightarrow\forall x,y\in A,\;\forall\varepsilon>0\;\exists\;n\in% \mathbb{N},\;\text{and }p_{1},...,p_{n}\in A,\;\text{such that }p_{1}=x,\;p_{n% }=y\;\text{and }d(p_{i},p_{i+1})<\varepsilon\;(i=1,...,n-1)$

Title characterization of connected compact metric spaces. CharacterizationOfConnectedCompactMetricSpaces 2013-03-22 14:05:37 2013-03-22 14:05:37 gumau (3545) gumau (3545) 12 gumau (3545) Theorem msc 54A05 LadderConnected