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\begin{center}\textbf{Problem Set 9 \hspace{.7in} Set Theory \& Topology \hspace{.7in} Due 4/27/16} \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.

\begin{enumerate}

\item {[Croom 9.2.1]} Prove that equivalence of loops is an equivalence relation.

\item {[Croom 9.2.2]} The identity element for $\Pi_1(X,x_0)$ is the homotopy class $[c]$ determined by the constant loop $c$.

\end{enumerate}


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