# Intersection of open dense subsets in a complete metric space is nonempty?

The proof for Baire category theorem in my book assumes that the intersection of dense subsets of a complete metric space is nonempty. Why can this be assumed, why is it true?

It's not true the way you stated it (think $$\Bbb Q$$ and the irrationals $$\Bbb P$$ in $$\Bbb R$$, e.g.)