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 ?
Each such morphism is necessarily an order-embedding.
The mapping [eta]: (S, *, [less than or equal to]) [right arrow] (P(S), *, [subset or equal to]), given by [eta](a) = a[down arrow] for each a [member of] S, is clearly an order-embedding of the poset (S, [less than or equal to]) into the poset (P(S), [subset or equal to]).
This means that [eta] is both monotone and an order-embedding.