View source for Anti-isomorphism of partially ordered sets

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]]