Definitions and preliminary discussions
Let D be an arbitrary domain1 with boundary Γ. Let E be a totally disconnected closed set contained in Γ. We suppose that w = f(z) is non-constant, single-valued and meromorphic in D. We associate with every point z0 of Γ the following: sets of values.
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- 1.Nevanlinna , p. 291.Google Scholar
- 2.Concerning notions of analytic continuation of algebraic character and (ordinary or essential) transcendental singularity, cf. Collingwood and Cartwright , pp. 99–103; Noshiro , pp. 43–73.Google Scholar
- 3.Iversen’s property of analytic functions has been systematically investigated by Stoïlow [1, 9].Google Scholar
- 1.Nevanlinna , p. 292.Google Scholar
- 2.This means that a is taken by w = f(z) only finite times in |z| < ∞.Google Scholar