Namespaces
Variants
Actions

Difference between revisions of "Antitone mapping"

From Encyclopedia of Mathematics
Jump to: navigation, search
(MSC 06A)
m (Implemented standard functional notation for easier reading.)
 
Line 3: Line 3:
 
''of partially ordered sets''
 
''of partially ordered sets''
  
A mapping $\phi$ of a [[partially ordered set]] $A$ into a partially ordered set $B$ such that if $a\leq b$ ($a,b\in A$), then $a\phi\geq b\phi$. The dual concept to an antitone mapping is an [[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=40158
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article