An Elementary Proof of a Theorem Concerning Infinitely Connected Domains
R. J. Sibner · Proceedings of the American Mathematical Society · 1973
Using classical complex function theory, it is shown that any infinitely connected plane domain is conformally equivalent to a domain whose isolated boundary components are analytic Jordan curves. This allows an elementary proof to be given of the result that a domain with countably many boundary components is conformally equivalent to a domain bounded by analytic Jordan curves.