1.1 Convex sets and combinations
A set is convex if together with any two points x, y it contains the segment [x, y], thus if
Examples of convex sets are obvious; but observe also that B0(z, ρ) ∪ A is convex if A is an arbitrary subset of the boundary of the open ball B0(z, ρ). As immediate consequences of the definition we note that intersections of convex sets are convex, affine images and pre-images of convex sets are convex, and if A, B are convex, then A + B and λA are convex.
Remark 1.1.1 For and λ, μ > 0 one trivially ...