Let $V$ be the [[set]] of all [[functions]] of $\mathbf{R}$ into $\mathbf{R}$. Let $W$ be the [[subset]], the continuous functions. Let $U$ be the set of differentiable functions of $\mathbf{R}$ into $\mathbf{R}$. - If $f, g$ are differentiable functions, then their sum $f+g$ is also differentiable. - If $c$ is a real number, then cf is differentiable. - The zero function is differentiable. So $U$ is a [[subspace]] of $V$. More specifically, $U$ is a [[subspace]] of $W$, because [[Differentiability implies Continuity]]