The Caratheodory Topology for Multiply Connected Domains II

Details The Caratheodory Topology for Multiply Connected Domains II The Caratheodory Topology for Multiply Connected Domains II

2011-03-13

arxiv.org/abs/1103.2537v4

Mathematics

Complex Variables

28 Pages, 3 Figures

Scientific paper

We continue our exposition concerning the Caratheodory topology for multiply connected domains 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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