I am currently learning topology from Munkres. The question below is an exercise in section 45.
Let $f_n\colon I\to \mathbb{R}$ be the function $f_n(x)=x^n$. The collection $F=\{f_n\}$ is pointwise bounded but the sequence $(f_n)$ has no uniformly convergent subsequence; at what point or points does $F$ fail to be equicontinuous.
Any help would be appreciated. Thank You.