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Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual $E^{\text{'}}$ of a locally convex space $E$ is the $\sigma (E^{\text{'}},E)$-closure of the union of countably many $\sigma (E^{\text{'}},E)$-relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.