Consider the linear spacet $\mathcal{F}(\mathbb{R}^n)$ of all real functions defined in $\mathbb{R}^n$. It is well known that the subspace $\mathcal{C}(\mathbb{R}^n)$ of all real valued continuous function defined in $\mathbb{R}^n$ is stable with respect to the uniform (convergence) limit of elements in $\mathcal{C}(\mathbb{R}^n)$.

**Question 1:** Which is the **smallest set** (with respect to inclusion relation) containing $\mathcal{C}(\mathbb{R}^n)$ and stable with respect to **pointwise convergence**?

**Question 2:** Which is the **smallest linear subspace** of $\mathcal{F}(\mathbb{R}^n)$ which is stable with respect to **pointwise convergence**?