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Pointwise order

From Encyclopedia of Mathematics
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The 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 $$ f \le g \Leftrightarrow \forall x \in X\,,\ f(x) \le g(x) \ . $$

How to Cite This Entry:
Pointwise order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pointwise_order&oldid=36146