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2014 | 12 | 5 | 721-741
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The Carathéodory topology for multiply connected domains II

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We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result which establishes several equivalent conditions for boundedness. This allows us to extend the notions of convergence and equicontinuity to families of functions defined on varying domains.
  • [1] Ahlfors L.V., Lectures on Quasiconformal Mappings, Van Nostrand Mathematical Studies, 10, Van Nostrand, Toronto, 1966
  • [2] Beardon A.F., Pommerenke Ch., The Poincaré metric of plane domains, J. London Math. Soc., 1978, 18(3), 475–483
  • [3] Carleson L., Gamelin T.W., Complex Dynamics, Universitext Tracts Math., Springer, New York, 1993
  • [4] Comerford M., Short separating geodesics for multiply connected domains, Cent. Eur. J. Math., 2011, 9(5), 984–996
  • [5] Comerford M., A straightening theorem for non-autonomous iteration, Comm. Appl. Nonlinear Anal., 2012, 19(2), 1–23
  • [6] Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340
  • [7] Conway J.B., Functions of One Complex Variable, Grad. Texts in Math., 11, Springer, New York-Heidelberg, 1972
  • [8] Epstein A.L., Towers of Finite Type Complex Analytic Maps, PhD thesis, CUNY Graduate School, 1993
  • [9] Herron D.A., Liu X.Y., Minda D., Ring domains with separating circles or separating annuli, J. Analyse Math., 1989, 53, 233–252
  • [10] Keen L., Lakic N., Hyperbolic Geometry from a Local Viewpoint, London Math. Soc. Stud. Texts, 68, Cambridge University Press, Cambridge, 2007
  • [11] Lang S., Complex Analysis, 3rd ed., Grad. Texts in Math., 103, Springer, New York, 1993
  • [12] McMullen C.T., Complex Dynamics and Renormalization, Ann. of Math. Stud., 135, Princeton University Press, Princeton, 1994
  • [13] Newman M.H.A., Elements of the Topology of Plane Sets of Points, 2nd ed., Cambridge University Press, Cambridge, 1961
  • [14] Pommerenke Ch., Uniformly perfect sets and the Poincaré metric, Arch. Math., 1979, 32(2), 192–199
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