Uniform convergence but limit not continuous

Question

i wanted to know if someone have an example of sequence of functions converging uniformly but such that the limit function (f) is not continuous .

Answer 1

Take a discontinuous function $f$ and consider the constant sequence $(f)_{n\in \mathbb{N}}$. That sequence converges uniformly to $f$, which is not continuous.

As pointed out by @JoséCarlosSantos this is the simplest possible example.