# Difference between revisions of "Isotone mapping"

From Encyclopedia of Mathematics

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− | 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. [[ | + | 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==== | ====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. [[ | + | 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]] | [[Category:Order, lattices, ordered algebraic structures]] |

## Revision as of 22:50, 26 October 2014

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).

**How to Cite This Entry:**

Isotone mapping.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Isotone_mapping&oldid=33613

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article