Question

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

Answer 1

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

Answer 2

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.