54-00-LadderConnected.tex

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\pmcomment{trigger rebuild}
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\pmrelated{CharacterizationOfConnectedCompactMetricSpaces}

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% Fri Oct  3 11:00:53 2003 -- should check at some point to see whether the replaced versions are actually used at all, I don't think so
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\begin{document}
{\bf Definition}
Suppose $X$ is a topological space. Then 
$X$ is called {\bf 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 $q\in U_N$.
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\end{document}