Namespaces
Variants
Actions

Difference between revisions of "Antitone mapping"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
m (Implemented standard functional notation for easier reading.)
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 +
{{TEX|done}}{{MSC|06A}}
 +
 
''of partially ordered sets''
 
''of partially ordered sets''
  
A mapping <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012730/a0127301.png" /> of a partially ordered set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012730/a0127302.png" /> into a partially ordered set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012730/a0127303.png" /> such that if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012730/a0127304.png" /> (<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012730/a0127305.png" />), then <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012730/a0127306.png" />. The dual concept to an antitone mapping is an [[Isotone mapping|isotone mapping]].
+
A mapping $ \phi $ of a [[partially ordered set]] $ A $ into a partially ordered set $ B $ such that if $ a \leq b $ (where $ a,b \in A $), then $ \phi(a) \geq \phi(b) $. The dual concept to an antitone mapping is an [[isotone mapping]].

Latest revision as of 02:57, 9 January 2017

2010 Mathematics Subject Classification: Primary: 06A [MSN][ZBL]

of partially ordered sets

A mapping $ \phi $ of a partially ordered set $ A $ into a partially ordered set $ B $ such that if $ a \leq b $ (where $ a,b \in A $), then $ \phi(a) \geq \phi(b) $. The dual concept to an antitone mapping is an isotone mapping.

How to Cite This Entry:
Antitone mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Antitone_mapping&oldid=12056
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article