Let $E_{i}$ be a nested compact subsequence s.t $\forall i E_i\geqslant r$ for $r>0$. How can we show that this implies that $\bigcap_{i=1}^\infty E_i$ also has parameter bigger than $r$?
the diameter of nested compact sequence
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real-analysis
metric-spaces
compactness
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0I think that you mean *diameter*, not *parameter*. – 2012-09-19