Let R be a metric space with usual metric \(\Large A_{n}= \left(\frac{-1}{n},\frac{1}{n}\right) \). Then \(\Large\bigcap\limits_{n=1}^{\infty}A_{n}\) is
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\(\Large A_{n}= \left(\frac{-1}{n},\frac{1}{n}\right) \)
Then \(\Large\bigcap\limits_{n=1}^{\infty}A_{n}=\{ 0 \}\)
This is not a open set in R.
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