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Isomorphism is a very general concept which appears in several areas of mathematics. Formally, an isomorphism is Bijective Morphism. Informally, an isomorphism is a map which preserves sets and relations among elements.

A space isomorphism is a Vector Space in which addition and scalar multiplication are preserved. An isomorphism of a Topological Space is called a Homeomorphism.

Two groups $G_1$ and $G_2$ with binary operators $+$ and $\times$ are isomorphic if there exists a map $f:G_1\mapsto G_2$ which satisfies

f(x+y)=f(x)\times f(y).

An isomorphism preserves the identities and inverses of a Group. A Group which is isomorphic to itself is called an Automorphism.

See also Automorphism, Ax-Kochen Isomorphism Theorem, Homeomorphism, Morphism

© 1996-9 Eric W. Weisstein