Van de Vel's Theory on Convexity Structures says a TVS is uniform iff it is locally convex:
3.10.1. Proposition. Let $X$ be a topological vector space, equipped with the standard convexity and with the canonical translation-invariant uniformity. Then $X$ is uniform iff it is locally convex. If, in addition, $X$ is (topologically) metrizable, then it is metrizable as a convex structure.
Wikipedia says a TVS is uniform:
a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis. As the name suggests the space blends a topological structure (a uniform structure to be precise) with the algebraic concept of a vector space.
So I guess I mess things up again. What am I missing?
Thanks and regards!