Chapter II

Convex sets and locally convex spaces

In §§ 2 to 7 of this chapter, we shall be concerned only with vector spaces and affine spaces over the field of real numbers $\mathbf{R}$, and when we speak of a vector space or an affine space without giving its division ring of scalars explicitly, then it is to be understood that this division ring is the field $\mathbf{R}$. For vector spaces on $\mathbf{C}$, see § 8.