I am fairly new on the concept of uniform convergence and I have the following basic question.
Let $(f_n)$ be a sequence of functions defined on a set $A \subseteq \mathbf{R}$ with $\lim_{n \rightarrow \infty}f_n = f$ uniformly on $A$. Is it true that $f_n$ converges uniformly to $f$ on any subset of $A$? If not, can someone provide a counterexample?