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 $Y$.

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

▾ Preordering relation

▾ Partial ordering relation

▾ Partially ordered set

▾ Isotone map

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

▾ Preordering relation

▾ Partial ordering relation

▾ Partially ordered set

▾ Isotone map

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 $Y$.

An D427: Isotone map $f : X \to Y$ from $P_X$ to $P_Y$ is an