Exercise 2, § 1

Let $K$ be a non-discrete topological division ring, $K_0$ the division ring $K$ with the discrete topology. The discrete topology on $K_0$ is compatible with its additive group structure, and when we consider $K_0$ as a vector space over $K$, it satisfies the axioms (EVT'_II) and (EVT'_III) but not (EVT'_I).