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Pointwise order

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The order on the set 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 $$ f \le g \Leftrightarrow \forall x \in X\,,\ f(x) \le g(x) \ . $$

See also: Pointwise operation.

References

[1] B. A. Davey, H. A. Priestley, Introduction to lattices and order, 2nd ed. Cambridge University Press (2002) ISBN 978-0-521-78451-1 Zbl 1002.06001
How to Cite This Entry:
Pointwise order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pointwise_order&oldid=36148