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\begin{center}\begin{large}\textbf{Math 131 - Problem Set 4\\
Due Tuesday, Oct 2}\end{large}\end{center}



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\noindent From Munkres:  23.2, 23.5, 23.9, 24.1, 24.2, 24.3, 26.2


\begin{enumerate} 

\item Let $X$ be a topological space and $A \subset X$ any subset. Define an operation $\Psi$ on subsets of $X$ by 
$$\Psi(A) = \overline{\text{int}(A)} \, \cap \, \overline{\text{int}(X \setminus A)}.$$
Show that for any subset $A \subset X$, $\Psi(\Psi(A)) = \emptyset$.

\end{enumerate}

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