Let X be a first countable space and let A be a subset of X. Then the following are true:
(1) (Sequence Lemma) A point x∈¯A if and only if there is a sequence of points of A converging to x.
(2) (Continuity Versus Sequential Continuity) Let f:X→Y . Then f is continuous if and only if f is sequentially continuous.
- Voclasses