Embedding

In mathematics, an embedding is one instance of some mathematical object contained within another instance, such as a group which is a subgroup.

In domain theory[?], an embedding is a complete partial order F in [X -> Y] is an embedding if

1. For all x1, x2 in X, x1 <= x2 <=> F x1 <= F x2 and
2. For all y in Y, x | F x <= y is directed[?].

("<=" is written in LaTeX as \sqsubseteq).

Based on an article from FOLDOC, used by permission.