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Difference between revisions of "Isotone mapping"

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(Category:Order, lattices, ordered algebraic structures)
(also: order-preserving mapping)
 
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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. [[Algebraic system|Algebraic system]]). An isotone mapping is also called a monotone mapping.
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''order-preserving mapping''
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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. [[Algebraic system]]). An isotone mapping is also called a monotone mapping.
  
  
  
 
====Comments====
 
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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]]).
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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]]).
  
 
[[Category:Order, lattices, ordered algebraic structures]]
 
[[Category:Order, lattices, ordered algebraic structures]]

Latest revision as of 11:11, 9 January 2016


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).

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