Difference between revisions of "Locally finite order"
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| − | An [[order relation]] on a partially ordered set $(X,{\le})$ in which every [[Interval and segment|interval]] is finite: for any given $a,b \in X$, there are only finitely many $x \in X$ such that $a \le x \le b$. | + | An [[order relation]] on a [[partially ordered set]] $(X,{\le})$ in which every [[Interval and segment|interval]] is finite: for any given $a,b \in X$, there are only finitely many $x \in X$ such that $a \le x \le b$. |
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| + | ====References==== | ||
| + | * Kung, Joseph P. S.; Rota, Gian-Carlo; Yan, Catherine H. ''Combinatorics. The Rota way''. Cambridge University Press (2009) {{ISBN|978-0-521-73794-4}} {{ZBL|1159.05002}} p.106 | ||
Latest revision as of 19:36, 7 November 2023
An order relation on a partially ordered set $(X,{\le})$ in which every interval is finite: for any given $a,b \in X$, there are only finitely many $x \in X$ such that $a \le x \le b$.
References
- Kung, Joseph P. S.; Rota, Gian-Carlo; Yan, Catherine H. Combinatorics. The Rota way. Cambridge University Press (2009) ISBN 978-0-521-73794-4 Zbl 1159.05002 p.106
How to Cite This Entry:
Locally finite order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Locally_finite_order&oldid=37012
Locally finite order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Locally_finite_order&oldid=37012