regionRegion2001-11-04 22:03:172007-05-31 01:31:43DefinitionComplex Analysis\usepackage{amssymb}
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A \emph{region} is a nonempty open subset of $\mathbb{C}$. Note that this definition is a \PMlinkescapetext{restriction} of that of \PMlinkname{domain}{Domain2} (as defined in complex analysis) to the complex plane. Some people prefer to use ``region'' instead of ``domain'' to avoid confusion with other mathematical definitions of domain. (The set theoretic definition of \PMlinkname{domain}{Domain} is also used in complex analysis.)
Regions play a major role in complex analysis since every nonempty open subset of $\mathbb{C}$ is the union of countably many connected components, each of which is a region.