Say I have some set $E\subset \mathbb{R}$, and an open cover $\cup A_i \supset E$. Is there a general algorithm that makes this cover disjoint?
How to make open covers disjoint in $\mathbb{R}$?
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real-analysis
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4In general, an open cover of $E$ does not have a disjoint subcover. What is meant by making "this" cover disjoint? – 2011-04-15
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1I imagine you intended $E\subset R$, not $E \in R$. – 2011-04-15
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1In addition to what user6312 wrote, you may want to look at the [Vitali covering lemma](http://en.wikipedia.org/wiki/Vitali_covering_lemma). – 2011-04-15