order-embedding

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order-embedding

A function f : D -> C is order-embedding iff for all x, y in D,

f(x) <= f(y) <=> x <= y.

I.e. arguments and results compare similarly. A function which is order-embedding is monotonic and one-to-one and an injection.

("<=" is written in LaTeX as \sqsubseteq).
References in periodicals archive ?
An order embedding from a poset (A, [[less than or equal to].sub.A]) to a poset (B, [[less than or equal to].sub.B]) is a mapping h: A [right arrow] B such that a [[less than or equal to].sub.A] a' iff h(a) [[less than or equal to].sub.B] h(a'), for all a, a' [member of] A.