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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Dense and open sets in R^n.

**Physics Forums | Science Articles, Homework Help, Discussion**