An embedding is a representation of a topological object, manifold, graph, field, etc. in a certain space in such a way that its connectivity or algebraic properties are preserved. For example, a field embedding preserves the algebraic structure of plus and times, an embedding of a topological space preserves open sets, and a graph embedding preserves connectivity. One space X is embedded in another space Y when the properties of Y restricted to X are the same as the properties of X. For example, the rationals are embedded in the reals, and the integers are embedded in the rationals. In geometry, the sphere is embedded in R^3 as the unit sphere.

Campbell's theorem | embeddable knot | embedded surface | extrinsic curvature | field | graph embedding | hyperboloid embedding | injection | manifold | Nash's embedding theorem