Since we have that every component of a region will be a domain, we have that every region has at most countably many components.
This definition has no particular relationship to the notion of an integral domain (http://planetmath.org/IntegralDomain), used in algebra. In number theory, one sometimes talks about fundamental domains in the upper half-plane, these have a different definition and are not normally open. In set theory, one often talks about the domain (http://planetmath.org/Function) of a function. This is a separate concept. However, when one is interested in complex analysis, it is often reasonable to consider only functions defined on connected open sets in , which we have called domains in this entry. In this context, the two notions coincide.
|Date of creation||2013-03-22 11:56:17|
|Last modified on||2013-03-22 11:56:17|
|Last modified by||drini (3)|