= Solution
{c}
On $E=\mathbb R$, take $f_n(x)=x$ and $g_n(x)=1/n$. Then $f_n\to f(x)=x$ with <uniform convergence>, because there is no error, and $g_n\to0$ with <uniform convergence>, with error $1/n$. Their products $f_ng_n=x/n$ converge <pointwise> to zero, but for every $n$ the choice $x=n$ gives $|f_n(x)g_n(x)|=1$. Thus \b[the products do not converge uniformly]. Here the first family consists of unbounded <functions>, exactly the missing hypothesis in the preceding estimate.
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