Topological stable rank of ${\mathcal{E}}^{\mathrm{\prime }}(\mathbb{R})$

The set ${\mathcal{E}}^{\mathrm{\prime }}(\mathbb{R})$ of all compactly distributions, with the operations of addition, convolution, multiplication by complex scalars, and with the strong dual topology is a topological algebra. In this article, it is shown that the topological stable rank of ${\mathcal{E}}^{\mathrm{\prime }}(\mathbb{R})$ is 2.