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=32930
Directed order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Directed_order&oldid=32930
This article was adapted from an original article by V.I. Ponomarev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article