x1 is a function mapping x2 (domain) to x3 (codomain) such that properties x4 (ka) of x2 are preserved in its image under x1 according to the rules/operations/relations of x3 corresponding to those of x2 by x1.
x1 is a ___-preserving function. Examples: Conformal mapping (angle-preserving locally), homogeneous function (roughly scale-preserving), homomorphism (facni), distinction-preserving function (ficystodraunju).