In functional analysis and related areas of mathematics, a Smith space is a complete compactly generated locally convex topological vector space having a universal compact set, i.e. a compact set which absorbs every other compact set (i.e. for some ). Smith spaces are named after Marianne Ruth Freundlich Smith, who introduced them as duals to Banach spaces in some versions of duality theory for topological vector spaces. All Smith spaces are stereotype and are in the stereotype duality relations with Banach spaces: Smith spaces are special cases of Brauner spaces.