Real Analysis/ Topology
Let $X$ and $Y$ be metric spaces and $f:X\rightarrow Y$. Prove using sequences that $f$ is continuous iff $f(\overline{E})\subset\overline{f(E)}$

Question

Real Analysis/ Topology
Let $X$ and $Y$ be metric spaces and $f:X\rightarrow Y$. Prove using sequences that $f$ is continuous iff $f(\overline{E})\subset\overline{f(E)}$

zzr0ck3r · Answer

I know how to prove this without using sequences but not sure how to go about it with them.

zzr0ck3r · Answer

The reason I put topology in the topic is because this is from a topology book but instead of metric space is said topological space, and instead of sequence it said nets. But I know it can be proved with the way it is here.