Isotone mapping

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A single-valued mapping of a partially ordered set into a partially ordered set 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).

How to Cite This Entry:
Isotone mapping. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article