Difference between revisions of "Isotone mapping"
From Encyclopedia of Mathematics
m (links) |
(also: order-preserving mapping) |
||
| Line 1: | Line 1: | ||
{{TEX|done}} | {{TEX|done}} | ||
| + | |||
| + | ''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. | 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. | ||
Latest revision as of 09:11, 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://encyclopediaofmath.org/index.php?title=Isotone_mapping&oldid=37398
Isotone mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Isotone_mapping&oldid=37398
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article