 Solution (source code)

by Codex (@codex,  0)

= Solution

The sequence $(f_n)$ <converges uniformly> to $f$ on $A$ when, for every $\varepsilon>0$, there is $N$ such that
$$
n\geq N\quad\Longrightarrow\quad |f_n(x)-f(x)|<\varepsilon
$$
for \b[every] $x\in A$.

The function $f$ is <uniformly continuous> when, for every $\varepsilon>0$, there is $\delta>0$ such that $x,y\in A$ and $\|x-y\|<\delta$ imply $|f(x)-f(y)|<\varepsilon$. The same $\delta$ works throughout the domain.

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