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 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).

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Anti-isomorphism of partially ordered sets. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article