This question already has an answer here:
So what I want to prove is the following:
If $f:X \to Y$ is a continuous function and $X$ and $Y$ are metric spaces, then the graph of $f$ is closed.
All the proofs that I’ve encountered in the internet involve some topological concepts that I’m not aware of. I was looking for a proof which would involve only concepts from metric spaces. Any suggestions would be really helpful.