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\@writefile{toc}{\contentsline {section}{\numberline {1}Compact subsets of metric spaces are closed.}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Rudin Ch 4, Problem 6.}{1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}If $f$ is defined on $E$, the \emph  {graph} $G$ of $f$ is the set of points $(x, f(x))$, for $x \in E$. In particular, if $E$ is a set of real numbers, and $f$ is real-valued, $G$ is a subset of the plane. Suppose $E$ is compact, and prove that $f$ is continuous on $E$ if and only if its graph is compact.}{1}}