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Omitting 'non uniformizable points' from the analogue of the Riemann surface of an analytic function of several complex variables we obtain a complex manifold. The following Theorem holds: Let M and M' be complex manifolds of the same dimension. Let N⊂M and N'⊂M' be analytic varieties. Then if there exists a proper analytic mapping T of M' into M which maps M'\N' one-to-one onto M\N then the fields of meromorphic functions in M and M' are isomorphic.
