1. The problem statement, all variables and given/known data (a) Prove that R, with the cocountable topology, is not first countable. (b) Find a subset A of R (with the cocountable topology), and a point z in the closure of A such that no sequence in A converges to z. 2. Relevant equations (The cocountable topology on R has as its closed sets all the finite and countable subsets of R). 3. The attempt at a solution I'm not really sure how to prove this. I know that if I could find a set and point meeting the conditions in part (b), then that would prove part (a), as in a first countable space X a point x belongs to the closure of a subset A of that space if and only if there is a sequence of points of A converging to x. However, I assume that I am expected to prove that R is not first countable with this topology some other way for part (a). Either way, I'm stuck!