x_{1} is a function mapping x_{2} (domain) to x_{3} (codomain) such that properties x_{4} (ka) of x_{2} are preserved in its image under x_{1} according to the rules/operations/relations of x_{3} corresponding to those of x_{2} by x_{1}.

x_{1} is a ___-preserving function. Examples: Conformal mapping (angle-preserving locally), homogeneous function (roughly scale-preserving), homomorphism (facni), distinction-preserving function (ficystodraunju).

- ficystodraunju
- x
_{1}is an injective function (distinctness-preserving function) from x_{2}(domain) to x_{3}(codomain). - facni
- x
_{1}is an n-ary operator/map which is distributive/linear/homomorphic in or over or from space/structure x_{2}, mapping to space or structure x_{3}, thereby producing a new space/structure x_{4}which is the 'union' of x_{2}and x_{3}endowed with x_{1}; x_{1}distributes over/through all of the operators of x_{2}.