30-00-ExtendedBoundary.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{ExtendedBoundary}
\pmcreated{2013-03-22 14:12:11}
\pmmodified{2013-03-22 14:12:11}
\pmowner{jirka}{4157}
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\pmtitle{extended boundary}
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\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{30-00}
\pmclassification{msc}{54-00}
\pmrelated{BoundaryInTopology}

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\begin{document}
\begin{defn}
Suppose that ${\mathbb{C}}$ is the complex plane and $G \subset {\mathbb{C}}$.  The {\em extended boundary} of $G$ denoted $\partial_\infty G$ is defined as
the boundary of $G$ plus the point at infinity if in fact $G$ is unbounded.
\end{defn}

The extended boundary of $G$ is really the boundary of $G$ 
in the extended complex plane (the one-point
compactification of ${\mathbb{C}}$).

\begin{thebibliography}{9}
\bibitem{Conway:complexI}
John~B. Conway.
{\em \PMlinkescapetext{Functions of One Complex Variable I}}.
Springer-Verlag, New York, New York, 1978.
\end{thebibliography}
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\end{document}