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