I need to show that a countable intersection of open and dense sets (the sets are open and dense at the same time) in R^n is dense in R^n.(adsbygoogle = window.adsbygoogle || []).push({});

Now I heard someone used in the exam a theorem called berr theorem for which the above statement is an immediate consequence.

We haven't learnt this theorem so I guess there's a simple way to prove this.

Thus far, what I can see is that for n=1, an open subset of R is an open interval (a,b) and a dense set in R is mainly Q or variation of the rationals set, for example the set: Q(sqrt(2)={c| c=a+sqrt(2)*b where a,b in Q} etc, but I don't see how can a set be both dense and open in R, I mean open sets alone aren't dense in R, cause their closure is the closed interval.

Any hints?

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# Dense and open sets in R^n.

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