# Directed order

From Encyclopedia of Mathematics

A binary relation on a set with the following properties: 1) if , , then , for any ; 2) for any , always ; and 3) for any there exists a such that , (the Moore–Smith property).

#### Comments

Many authors require a directed order to be a partial order (i.e. to satisfy the condition that and together imply , as well as 1) and 2) above), and also require the underlying set to be non-empty.

**How to Cite This Entry:**

Directed order.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Directed_order&oldid=14517

This article was adapted from an original article by V.I. Ponomarev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article