Difference between revisions of "Anti-isomorphism of partially ordered sets"
From Encyclopedia of Mathematics
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| − | 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 [[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 $ in $ A $ implies $ \phi(a) > \phi(b) $ in $ B $ (and similarly for the inverse). |
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[[Category:Order, lattices, ordered algebraic structures]] | [[Category:Order, lattices, ordered algebraic structures]] | ||
Latest revision as of 02:54, 9 January 2017
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 $ in $ A $ implies $ \phi(a) > \phi(b) $ 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=34360
Anti-isomorphism of partially ordered sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-isomorphism_of_partially_ordered_sets&oldid=34360
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article