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

Abstract

The set ${\mathcal{E}}^{\prime }(\mathbb{R})$ 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 ${\mathcal{E}}^{\prime }(\mathbb{R})$ is 2.

12 pages. In the new version, the typos which were discovered in the first version have been corrected, and an alternative proof of Prop.4.1 (suggested by Peter Wagner) has been added