Embedding

In mathematics, an embedding is one instance of a mathematical structure contained within another instance of a similar or larger structure, such as a group appearing as a subgroup of another group. The idea appears across many branches of mathematics, including topology, algebra, differential geometry and category theory. Formally, an object X is said to be embedded in an object Y when there is an injective, structure-preserving map from X into Y, though what counts as structure-preserving depends on context, for example a homeomorphism onto its image for topological spaces, or a ring homomorphism for fields. A familiar illustration is the chain of number systems, where the natural numbers embed into the integers, the integers into the rationals, the rationals into the reals, and the reals into the complex numbers, each an embedding in which the smaller system is naturally identified with its image inside the larger one. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/