# Locally finite order

From Encyclopedia of Mathematics

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=37022