The image of a linear operator has this property if and only if the operator’s adjoint is injective. The subspace spanned by finite linear combinations of a Schauder basis has this property. For a countable collection of sets that all have this property nowhere, their union (15[1])is called “meager,” (15[1])or (15[1])first category. (15[2])If open subsets (15[1])of a complete space (15[1]-5[1])have this property, then (-5[1])so does their countable intersection, by the (*) Baire category theorem. A space has this property in any (-5[1])of its compactifications. (-5[1])A countable collection of polynomials has this property in C[0, 1] (“C zero one”) by the (10[1])Stone-Weierstrass theorem, (10[1])so the latter space is separable. Two continuous functions that agree (10[1])on a set with this property must be the same, since adjoining limit points to one of these sets gives the whole space. (10[1]-5[1])For 10 points, give this property (10[1])of a subset whose closure is the entire space. ■END■ (10[2]0[10])