# Anti-isomorphism of partially ordered sets

From Encyclopedia of Mathematics

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=40157

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article