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).

This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

References in periodicals archive

Each such morphism is necessarily an order-embedding. In this section we show that [E.sub.[less than or equal to]]-injective objects in the category [PoSgr.sub.[less than or equal to]] are precisely the quantales.

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. If now [eta]([a.sub.1]) [omicron] ...

Injective hulls for posemigroups/Jarjestatud poolruhmade injektiivsed katted

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