Let $V$ be the [[set]] of all [[Function|functions]] of $\mathbf{R}$ into $\mathbf{R}$. Then $V$ is a [[vector space]] over $\mathbf{R}$. Let $W$ be the [[subset]] of [[Continuity on a Domain|continuous]] functions. - If $f, g$ are continuous functions, then $f+g$ is continuous. - If $c$ is a real number, then $c f$ is continuous. - The zero function is continuous. So $W$ is a subspace of the vector space of all functions of $\mathbf{R}$ into $\mathbf{R}$, i.e. $W$ is a subspace / function space of $V$.