The Riemann Mapping Theorem and Simple Connectedness in the Plane

  • Raghavan Narasimhan


In this chapter, we shall prove that any simply connected open set in ℂ, which is not all of ℂ, is analytically isomorphic to the unit disc D= {z∊ℂ∣∣z∣<1}. The proof will also enable us to characterize simple connectedness in several ways.


Riemann Surface Blaschke Product Simple Connectedness Uniformization Theorem Riemann Mapping Theorem 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Raghavan Narasimhan
    • 1
  1. 1.Department of MathematicsThe University of ChicagoChicagoUSA

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