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The [[Order (on a set)|order]] on the section of functions with values in a [[partially ordered set]].  If $f$ and $g$ are functions from $X$ to $Y$, where $(Y,<)$ is ordered, then there is an [[order relation]] on $Y^X$ defined by
$$
f \le g \Leftrightarrow \forall x \in X\,,\ f(x) \le g(x) \ .
$$

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Pointwise order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pointwise_order&oldid=36144

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