View source for Isotone mapping

{{TEX|done}}

''order-preserving mapping''

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.



====Comments====
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]]).

[[Category:Order, lattices, ordered algebraic structures]]