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 and with binary operators and are isomorphic if there exists a map
which satisfies

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

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1999-05-26