Some Topology

  • Daniel Alpay


Topology intervenes in complex variables at various levels. First of all analytic functions are defined in open sets. Connectedness plays a key role in the proof of the uniqueness theorem for analytic functions. The space of functions analytic in an open set is endowed with the topology of uniform convergence on compact sets.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Daniel Alpay
    • 1
    • 2
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.Department of MathematicsChapman UniversityOrangeUSA

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