# embedding

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Related to Isometric embedding: Imbedding

## embedding

[em′bed·iŋ] (mathematics)

An injective homomorphism between two algebraic systems of the same type.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## embedding

(mathematics)One instance of some mathematical object
contained with in another instance, e.g. a group which is a
subgroup.

## embedding

(theory)(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).

(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).

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