n. a one-to-one correspondence between the elements of two or more sets that preserves the structural properties of the domain; a bijective homomorphism. For example, the bijective mapping from the integers to those rationals that are of the form n/1 retains the order of the elements, and the sum or product of the images of two elements equals the image of their sum or product; the logarithmic function is an isomorphism between the reals under addition and the positive reals under multiplication, since it is a bijection under which x=yz if and only if ln x = ln y + ln z. See also automorphism, dual isomorphism. Compare epimorphism, monomorphism.