In Rudin's Real and Complex Analysis (p. 97 in my 3rd edition), the following is stated as a corollary to Baire's Category Theorem:
"In a complete metric space, the intersection of any countable collection of dense $G_{\delta}$'s is again a dense $G_{\delta}$."
Proof: "This follows from the theorem, since every $G_{\delta}$ is the intersection of a countable collection of open sets, and since the union of countably many countable sets is countable."
I don't understand the word union in the argument. It seems like it should be intersection, as the theorem states that such an intersection is dense. Is this a typo or am I missing something?