Given two
partially ordered sets (
S, <=) and (
T, [=) an
order isomorphism from (
S, <=) to (
T, [=) is an
isomorphism from
S to
T that preserves the order, that is, it is a
bijection h :
S -> T such that for all
u and
v in
S it holds that
- h(u) [= h(v) if and only if u <= v.
If there is an order isomorphism between two partially ordered sets then these sets are called order isomorphic.
An order isomorphism from (S,<=) to itself is called an order automorphism
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