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