In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures. More at Wikipedia
Holomorphism - In mathematics, holomorphic functions are the central objects of study in complex analysis.
Homeomorphism - In the mathematical field of topology, a homeomorphism or topological isomorphism or bicontinuous function is a continuous function between two topological spaces that has a continuo...
continuous function - In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output.
diffeomorphism - In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds.