isomorphism

Formally,
an isomorphism is a homomorphism $f:A\to B$ that has an inverse homomorphism $g:B\to A$, such that $fg=1_B$ and $gf=1_A$.

Two structured sets are isomorphic, written $A\cong B$, if an isomorphism exists between them.

• an isometry is an isomorphism of metric spaces
• a homeomorphism is an isomorphism of topological spaces