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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

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Volume 12, Issue 5


Volume 13 (2015)

The Carathéodory topology for multiply connected domains II

Mark Comerford
Published Online: 2014-02-15 | DOI: https://doi.org/10.2478/s11533-013-0365-y


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.

Keywords: Carathéodory Topology; Meridians; Bounded family of pointed domains

MSC: 30C75; 30C20; 30C45

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About the article

Published Online: 2014-02-15

Published in Print: 2014-05-01

Citation Information: Open Mathematics, Volume 12, Issue 5, Pages 721–741, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0365-y.

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© 2014 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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