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\begin{center}\textbf{Problem Set 9 \hspace{.7in} Set Theory \& Topology \hspace{.7in} Due 4/26/18} \end{center}

\noindent You are expected to do the following problems to a high standard for full credit.  Each problem is worth 5 points.

\begin{enumerate}

\item {[Croom 9.2.1a]} Equivalence of loops is a reflexive relation.

\item {[Croom 9.2.1b]} Equivalence of loops is a symmetric relation.

\item {[Croom 9.2.1c]} Equivalence of loops is a transitive relation.

\item {[Croom 9.2.8]} A convex set $A$ in $\mathbb{R}^n$ is contractible to each point $x_0$ in $A$.

\end{enumerate}


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