Suppose $E\subset R$,if $E$ can be covered by a series of interval $\{I_{\lambda}\}_{\lambda\in \Lambda}$,then E can be covered by a countable subset series which are in $\{I_{\lambda}\}_{\lambda\in \Lambda}$ ?
E can be covered by a countable subset?
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real-analysis
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0Not correct. Consider the intervals $\{[a,a]\}_{a\in R}$. They cover $R$ but don't have a countable sub-cover. – 2012-09-24
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0you are right.Actually I should add up that the intervals are non-empty interiors. – 2012-09-24