isomorphism

n. identity or similarity of form or appearance (Biology)

In mathematics, an isomorphism (Greek: isos "equal", and morphe "shape") is a bijective map f such that both f and its inverse f −1 are homomorphisms, i.e., structure-preserving mappings.Informally, an isomorphism is a kind of mapping between objects, which shows a relationship between two properties or operations. If there exists an isomorphism between two structures, we call the two structures isomorphic. In a certain sense, isomorphic structures are structurally identical, if you choose to ignore finer-grained differences that may arise from how they are defined.
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Noun
1. (biology) similarity or identity of form or shape or structure
(synonym) isomorphy
(hypernym) similarity
(classification) biology, biological science

(n.)
A similarity of crystalline form between substances of similar composition, as between the sulphates of barium (BaSO4) and strontium (SrSO4). It is sometimes extended to include similarity of form between substances of unlike composition, which is more properly called homoeomorphism.
  

<mathematics> A bijective map between two objects which preserves, in both directions, any structure under consideration. Thus a `group isomorphism' preserves group structure; an order isomorphism (between posets) preserves the order relation, and so on. Usually it is clear from context what sort of isomorphism is intended.
(1995-03-25)