Directed order

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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).


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