Is this true that a locally convex topological (Hausdorff) vector space becomes a normed space when its local base has only one element, so only one Minkowski functional and so only one seminorm and hence norm.
2026-03-25 17:45:15.1774460715
Condition under which a locally convex topological vector space becomes a normed linear space
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This result was proved in 1935 by A. Kolmogoroff: The topology of a locally convex topological vector space is generated by a norm iff there exists a bounded neighborhood of $0$.