ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Binary endorelation
Preordering relation
Partial ordering relation
Partially ordered set
Isotone map
Definition D1819
Order isomorphism
Formulation 1
Let $P_X = (X, {\preceq}_X)$ and $P_Y = (Y, {\preceq}_Y)$ each be a D1103: Partially ordered set.
An D427: Isotone map $f : X \to Y$ from $P_X$ to $P_Y$ is an order isomorphism from $P_X$ to $P_Y$ if and only if $f$ is a D468: Bijective map from $X$ to $Y$.