ladder connected

Definition Suppose $X$ is a topological space. Then $X$ is called ladder connected provided that any open cover $\mathcal{U}$ of $X$ has the following property: If $p,q\in X$ , then there exists a finite number of open sets $U_{1},\ldots,U_{N}$ from $\mathcal{U}$ such that $p\in U_{1}$ , $U_{1}\cap U_{2}\neq\emptyset$ , $\ldots$ , $U_{N-1}\cap U_{N}\neq\emptyset$ , and $q\in U_{N}$ .

Title	ladder connected
Canonical name	LadderConnected
Date of creation	2013-03-22 14:00:29
Last modified on	2013-03-22 14:00:29
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	6
Author	mathcam (2727)
Entry type	Definition
Classification	msc 54-00
Related topic	CharacterizationOfConnectedCompactMetricSpaces