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Let $K$ be a field with a Krull valuation $\left|\right|$ and value group $G\ne \left\{1\right\}$, and let $B_K$ be the valuation ring. Theories about spaces of countable type and Hilbert-like spaces in [1] and spaces of continuous linear operators in [2] require that all absolutely convex subsets of the base field $K$ should be countably generated as $B_K$-modules. By [1] Prop....