Math 6510 • Differentiable Manifolds

Let \(X\) be a topological space and \(x_0\in X\) a basepoint.
\begin{enumerate}
\item[(a)] Define \(\pi_1(X,x_0)\) (describe it as a set and define the group
operation; you don't have to prove that it is well defined or that it is a group).
\item[(b)] If \(X\) is path-connected and \(x_1\in X\) prove that
\(\pi_1(X,x_0)\cong\pi_1(X,x_1)\) (write down an explicit isomorphism and check that
it works).
\end{enumerate}