Let formula_30 be a topological vector space over a number field formula_76 (of real numbers formula_77 or complex numbers formula_78). Consider its strong dual space formula_79, which consists of all continuous linear functionals formula_35 and is equipped with the strong topology formula_81, "i.e.", the topology of uniform convergence on bounded subsets in formula_30. The space formula_79 is a topological vector space (to be more precise, a locally convex space), so one can consider its strong dual space formula_84, which is called the strong bidual space for formula_30. It consists of all