Isomorphic

Definition · applies to mathematical structures · also called $\cong$

High school

Two structures are isomorphic if the two structures are the same except for the names of their elements.

Undergraduate

Two structures (groups, vector spaces, graphs, and so on) are isomorphic if there is a bijection between the two structures that preserves the structure, and whose inverse also preserves the structure.

Examples

Examples

• $\reals^2$ and $\mathbb{C}$, as real vector spaces Undergraduate

Distinctions involving this term

• Types of sameness: Mathematics has many ways to say that two objects are “the same.” Equal objects are the same object. The other words describe objects that are different but “the same in some respect,” and each one depends on what respect is meant.

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