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Revision difference : order-preserving map
Version 2 Version 1
Order-preserving map from a poset $L$ to a poset $M$ is a function $f$ such that Order preserving map from a poset $L$ to a poset $M$ is a function $f$ such that
$$\forall x,y\in L:(x\ge y\implies f(x)\ge f(y)).$$ $$\forall x,y\in L:(x\ge y\implies f(x)\ge f(y)).$$
Order-preserving maps are also called monotone functions or monotonic functions.