Isotone relations and the fixed point property for posets

AbstractA strengthened form of the fixed point property for posets is presented, in which isotone functions are replaced by more general isotone relations. For finite posets, this ‘relational fixed point property’ turns out to be equivalent to dismantlability. But an example shows that not every infinite poset with the relational fixed point property is dismantlable. Applications to quotients and direct products are given