摘要：We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation in tangle space which is a set of real tangles with analytic structure and describe the recombination as the action of some enzymes on tangle space.
