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The Carathéodory topology for multiply connected domains II

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Comerford M.

Open Mathematics

2014

tom 12

nr 5

721-741

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.

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1 Open Mathematics

1 Comerford M.

1 2014

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The Carathéodory topology for multiply connected domains II