A Set is Closed in a First Countable Space iff it contains all its Sequential Limits
# Statement
Suppose $(X, \tau)$ is a First Countable Space. Then $K \subset X$ is Closed If and Only If $$K \supset {x : \exists (x_n) \subset K \text{ s.t. } x_{n} \to x}$$ That is, $K$ contains all its sequential limits.