Difference between revisions of "Anti-isomorphism of partially ordered sets"
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| − | A bijective antitone mapping of a partially ordered set $A$ into a partially ordered set $B$, for which the inverse is also antitone, i.e. a one-to-one mapping $\phi : A \rightarrow B$ such that $a < b$ ( | + | A [[bijection|bijective]] [[antitone mapping]] of a [[partially ordered set]] $A$ into a partially ordered set $B$, for which the [[inverse mapping]] is also antitone, i.e. a [[Injection|one-to-one mapping]] $\phi : A \rightarrow B$ such that $a < b$ ($a,b \in A$) implies $a\phi > b\phi$ in $B$ (and similarly for the inverse). |
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| + | [[Category:Order, lattices, ordered algebraic structures]] | ||
Revision as of 18:23, 8 November 2014
A bijective antitone mapping of a partially ordered set $A$ into a partially ordered set $B$, for which the inverse mapping is also antitone, i.e. a one-to-one mapping $\phi : A \rightarrow B$ such that $a < b$ ($a,b \in A$) implies $a\phi > b\phi$ in $B$ (and similarly for the inverse).
How to Cite This Entry:
Anti-isomorphism of partially ordered sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-isomorphism_of_partially_ordered_sets&oldid=34359
Anti-isomorphism of partially ordered sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-isomorphism_of_partially_ordered_sets&oldid=34359
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article