Pre-order
From Encyclopedia of Mathematics
quasi-order, pre-ordering, quasi-ordering
A reflexive and transitive binary relation on a set. If 
is a pre-order on a set 
, then the relation 
if and only if 
and 
, 
, is an equivalence on 
. The pre-order 
induces an order relation (cf. also Order (on a set)) on the quotient set 
.
How to Cite This Entry:
Pre-order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pre-order&oldid=31681
Pre-order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pre-order&oldid=31681
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article