## If $f_m$ is a sequence of continuous functions which converges to a function. then that function if continuous as well.

I was looking for the proof is this theorem, but I couldn’t find it anywhere.

the theorem is stated formally:

If $$f_m$$ is a sequence of continuous functions defined on $$D$$ (subset of $$R$$) such that $$f_m \to f$$ uniformly on $$D$$ then $$f$$ is continous.