A single-valued mapping $\phi$ of a partially ordered set $A$ into a partially ordered set $B$ preserving the order. Isotone mappings play the role of homomorphisms of partially ordered sets (considered as algebraic systems with a single relation, cf. Algebraic system). An isotone mapping is also called a monotone mapping.
Such mappings are also called increasing or order-preserving. The term "monotone" generally denotes a mapping which may be either isotone or antitone (cf. Antitone mapping).
Order-preserving mapping. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Order-preserving_mapping&oldid=37399