= Pointwise multiplication
{title2=$(fg)(x)=f(x)g(x)$}
For <functions> $f,g:X\to\mathbb R$ or $\mathbb C$, their <pointwise multiplication> is the <function> $fg$ with $(fg)(x)=f(x)g(x)$. Both values are evaluated at the same input before multiplication. If $f(x)=x+1$ and $g(x)=x^2$, then $(fg)(2)=3\cdot4=12$ and $(fg)(x)=x^3+x^2$.
Together with <pointwise addition>, this makes the <continuous functions> on a <topological space> into an <algebra over a field>. Closure properties still need checking for other <function spaces>: two <L2 space> functions need not have an <L2 space> product. For example, $f(x)=g(x)=x^{-1/3}$ on $(0,1)$ have integrable squares, but $(fg)^2=x^{-4/3}$ is not integrable. The ambient <function space> matters.
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