Difference between revisions of "Pointwise order"
From Encyclopedia of Mathematics
(Start article: Pointwise order) |
(cite Davey & Priestley (2002)) |
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f \le g \Leftrightarrow \forall x \in X\,,\ f(x) \le g(x) \ . | f \le g \Leftrightarrow \forall x \in X\,,\ f(x) \le g(x) \ . | ||
$$ | $$ | ||
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| + | See also: [[Pointwise operation]]. | ||
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| + | ====References==== | ||
| + | <table> | ||
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> 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}}</TD></TR> | ||
| + | </table> | ||
Revision as of 22:40, 7 January 2015
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 $$ f \le g \Leftrightarrow \forall x \in X\,,\ f(x) \le g(x) \ . $$
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=36144
Pointwise order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pointwise_order&oldid=36144