I have come up with an example when I trying to learn what first countability means(adsbygoogle = window.adsbygoogle || []).push({});

It says(from wikipedia)

In a metric space, for any point x, the sequence of open balls around x with radius 1/n form a countable neighbourhood basis [tex]\mathcal{B}(x) = \{ B_{1/n}(x) ; n \in \mathbb N^* \}.[/tex] This means every metric space is first-countable.

According to definition of nhd basis we can express every open set can be expressed as a union of elts of nhd basis But for example [tex] \{ B_{ sqrt{2} }(x) [/tex] can not be expressed in this way

Here is the question

which point did i miss?

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# First countability

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