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Find and proof an open cover of $(0, 1)$ that has no finite subcover.

I need to find an example and also proof the example.

Thank you.

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up vote 4 down vote accepted

$(0,1)=\cup_{n=1}^{\infty}(\frac{1}{n},1-\frac{1}{n})$ is an open cover but has no finite subcover

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To modify this interval to (1,2), would you just add 1 to each of those terms? e.g. (1+$1 \over n$, 2 - $1 \over n$)? – Nick Sep 24 '13 at 4:51

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