From a conceptual point of view, all notions related to topological vector spaces should match the topology. For example, instead of considering all linear maps (also called functionals) V → → W , maps between topological vector spaces are required to be continuous. In particular, the (topological) dual space V ∗ ∗ consists of continuous functionals V → → R (or to C ). The fundamental Hahn–Banach theorem is concerned with separating subspaces of appropriate topological vector spaces by continuous functionals.