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Embed \Em*bed"\ ([e^]m*b[e^]d"), v. t. [imp. & p. p. {Embedded};
p. pr. & vb. n. {Embedding}.] [Pref. em- bed. Cf. {Imbed}.]
To lay as in a bed; to lay in surrounding matter; to bed; as,
to embed a thing in clay, mortar, or sand.
[1913 Webster]

1. One instance of some mathematical object
contained with in another instance, e.g. a {group} which is a
subgroup.

2. ({domain theory}) 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}).

(1995-03-27)

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