# The Carathéodory topology for multiply connected domains II

Open Mathematics (2014)

- Volume: 12, Issue: 5, page 721-741
- ISSN: 2391-5455

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topMark Comerford. "The Carathéodory topology for multiply connected domains II." Open Mathematics 12.5 (2014): 721-741. <http://eudml.org/doc/269107>.

@article{MarkComerford2014,

abstract = {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.},

author = {Mark Comerford},

journal = {Open Mathematics},

keywords = {Carathéodory Topology; Meridians; Bounded family of pointed domains; Carathéodory topology; meridians; bounded family of pointed domains},

language = {eng},

number = {5},

pages = {721-741},

title = {The Carathéodory topology for multiply connected domains II},

url = {http://eudml.org/doc/269107},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Mark Comerford

TI - The Carathéodory topology for multiply connected domains II

JO - Open Mathematics

PY - 2014

VL - 12

IS - 5

SP - 721

EP - 741

AB - 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.

LA - eng

KW - Carathéodory Topology; Meridians; Bounded family of pointed domains; Carathéodory topology; meridians; bounded family of pointed domains

UR - http://eudml.org/doc/269107

ER -

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