Convexity in Real Projective Space

In this introductory chapter we look at ordinary convexity in ℝ n by embedding ℝ n into real projective space ℝℙ n . In this way convexity becomes invariant under projective mappings. In Section 1.1 we discuss very briefly conditions that characterize convexity in ℝ n . In Section 1.2 we introduce fundamental geometric concepts in real projective space ℝℙ n such as projective lines, projective hyperplanes and projective mappings. In Section 1.3 we define convexity in ℝℙ n and study fundamental properties of convex sets. We define the polar of a subset in ℝℙ n and relate convex sets and linearly convex sets.