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\begin{center}\textbf{Problem Set 7 \hspace{.7in} Set Theory \& Topology \hspace{.7in} Due 4/12/18} \end{center}

\noindent You are expected to do the following problems to a high standard (i.e., at least well enough to be published in a textbook) for full credit.  Four of these problems will be selected (by Jon) for grading, with each worth 5 points.

\begin{enumerate}

\item Every subspace of a normal space is normal.

\item {[Baker 7.3.10]} Every closed subset of a normal space is normal.

\item {[Baker 8.2.2]} Give a direct proof (without using Theorem 8.2.2) that every metric space is regular.

\item {[Baker 8.2.4]} Complete the proof of Theorem 8.2.5.

\end{enumerate}


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