The Carathéodory topology for multiply connected domains II
Date of Original Version
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. © 2014 Versita Warsaw and Springer-Verlag Wien.
Central European Journal of Mathematics
Comerford, Mark. "The Carathéodory topology for multiply connected domains II." Central European Journal of Mathematics 12, 5 (2014): 721-741. doi:10.2478/s11533-013-0365-y.