Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or "to shape."

Formally, an isomorphism is bijective morphism. Informally, an isomorphism is a map that preserves sets and relations among elements. "A is isomorphic to B" is written A=B. Unfortunately, this symbol is also used to denote geometric congruence.

An isomorphism from a set of elements onto itself is called an automorphism.

See also

Automorphism, Ax-Kochen Isomorphism Theorem, Graph Isomorphism, Homeomorphism, Isomorphic Graphs, Isomorphic Groups, Morphism Explore this topic in the MathWorld classroom

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Isomorphism." From MathWorld--A Wolfram Web Resource.

Subject classifications