Let $C(\mathbb{R}^n;\mathbb{R}^d)$ be the space of continuous functions with the uniform-convergence on compacts topology.  What are function spaces $X$ building on $C(\mathbb{R}^n;\mathbb{R}^d)$?

 - $X$ properly contains $C(\mathbb{R}^n;\mathbb{R}^d)$,
 - The subspace topology on $C(\mathbb{R}^n;\mathbb{R}^d)$ (wrt X) agrees with the topology of uniform convergence on compacts,
 - The elements of $X$ are functions from $\mathbb{R}^n$ to $\mathbb{R}^d$
 - $C(\mathbb{R}^n;\mathbb{R}^d)$ is dense in $X$.