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 .
Pre-order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pre-order&oldid=15209