\begin{definition}[Definition:Homotopy Class/Path]
Let $T = \struct {S, \tau}$ be a topological space.
Let $f: \closedint 0 1 \to S$ be a path in $T$.
The '''homotopy class''' of the path $f$ is the homotopy class of $f$ relative to $\set {0, 1}$.
That is, the equivalence class of $f$ under the equivalence relation defined by path-homotopy.
\end{definition}