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Since + $\emptyset$ and $\R$ are open, it follows that $\emptyset$ and $\R$ are closed as well. + + \begin{enumerate}[label=\emph{(\alph*)}] + \item Let $a,b \in \R$ with $a < b$. Prove that $[a,b]$ is closed. + \item Is the set $\Z \subset \R$ closed? Provide a proof to substantiate your claim. + \item Is the set of rationals $\Q \subset \R$ closed? Provide a proof to substantiate your claim. + \end{enumerate} +\end{tcolorbox} + +\begin{enumerate}[label=\emph{(\alph*)} + \item The complement of $[a,b]$ is equal to the union of $(-\infty, a)$ and $(b, \infty)$. So, we have to prove + that both these sets are open. But we have already done so in the assignment of the previous week, so I'll just + leave it at that. + \item + \item +\end{enumerate} + +\end{document}

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