Published online by Cambridge University Press: 24 October 2008
1. In the theory of conformal mapping, there are many problems associated with domains of infinite connectivity which have not yet been fully explored. We consider, in this paper, some of these problems in relation to domains in the closed complex plane. In the following all domains are assumed to be plane domains and all mappings to be (1, 1) and conformal in the domains in which they are defined.