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.
Canonical name	CharacterizationOfConnectedCompactMetricSpaces
Date of creation	2013-03-22 14:05:37
Last modified on	2013-03-22 14:05:37
Owner	gumau (3545)
Last modified by	gumau (3545)
Numerical id	12
Author	gumau (3545)
Entry type	Theorem
Classification	msc 54A05
Related topic	LadderConnected