\begin{definition}[Definition:Multiplication of Homotopy Classes of Paths]
Let $T = \struct {S, \tau}$ be a topological space.
Let $\alpha, \beta$ be homotopy classes of paths in $T$.
Let $f, g: \closedint 0 1 \to S$ be representative paths for $\alpha$ and $\beta$ respectively.
Let $\map f 1 = \map g 0$.
The '''product of the homotopy classes''' $\alpha$ and $\beta$ is the homotopy class of the concatenated path $f * g$.
\end{definition}