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\begin{document}

\centerline {\bf Math 523b - Homework 1} 

\bigskip

\begin{enumerate}

\item Let $X$ be a topological space and $A$ and $B$ subsets of it. 
For each of the following statements either prove it or disprove it 
by giving a counterexample. 
  \begin{enumerate}
  \item $\overline {A \cup B}= \overline{A} \cup \overline{B}$
  \item $\overline {A \cap B}= \overline{A} \cap \overline{B}$
  \end{enumerate}

\item Folland, problem 5, page 118.

\item Folland, problem 10, page 118.

\item Folland, problem 15, page 123.

\item Folland, problem 16, page 123.

\item Folland, problem 22, page 123.

\item Folland, problem 28, page 124.

\item Folland, problem 40, page 130.

\item Folland, problem 43, page 130.

\end{enumerate}

\end{document}
\end
