Exercise 2, § 1

On the real line $\mathbf{R}$, carrying the additive uniformity, show that as $V$ runs through the filter of entourages of $\mathbf{R}$ the sets $V(\mathbf{Z})$ do not form a fundamental system of neighbourhoods of the set $\mathbf{Z}$ of rational integers.* (Cf. § 4, no. 3, Corollary to Proposition 4).