continuous correspondences on a Riemann surface, whether algebraic or not, uithout recourse to transcendental considerations.(d) Open manifolds.Here an adaptation of a reasoning due to Alex- ander leads to the solution of the question.(e) One-sided manifolds.They may be replaced by suitable two-sided open manifolds.(f) Conformal representation.Julia's theorem on the conformal repre- sentation of a plane region on a part of itself,3 together with Ritt's ex- tension4 and other generalizations for functions of several complex varia- bles can be readily obtained by our method.
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James W. Alexander (1923) studied this question.