\begin{definition}[Definition:Homotopy Class]
Let $X$ and $Y$ be topological spaces.
Let $K \subseteq X$ be any subset.
Let $f : X \to Y$ be a continuous mapping.
The '''homotopy class''' or '''$K$-homotopy class''' of $f$ is the equivalence class of $f$ under the equivalence relation defined by homotopy relative to $K$.
\end{definition}