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Difference between revisions of "Isotone mapping"

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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|Antitone 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|Antitone mapping]]).
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[[Category:Order, lattices, ordered algebraic structures]]

Revision as of 20:14, 13 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