Continuity and Prime Ends

  • Christian Pommerenke
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 299)

Abstract

Let f map the unit disk D conformally onto \( G \subset \hat {\Bbb C} = {\Bbb C} \cup \left\{ \infty \right\}\). In this chapter, we study the problem whether it is possible to extend f to some or all points ζ ∈ T = D by defining
$$ f\left( \zeta \right) = \mathop {\lim }\limits_{z \to \zeta } f\left( z \right) \in \hat {\Bbb C}.$$
(1)

Keywords

Jordan Curve Junction Point Jordan Domain Radial Limit Angular Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Christian Pommerenke
    • 1
  1. 1.Fachbereich MathematikTechnische UniversitätBerlin 12Germany

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