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 20:50, 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://encyclopediaofmath.org/index.php?title=Isotone_mapping&oldid=33613
Isotone mapping. Encyclopedia of Mathematics. URL: http://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