A gentle introduction to the geometry of convex sets inn-dimensional spaceGeometry of Convex Setsbegins with basic definitions of the concepts of vector addition and scalar multiplication and then defines the notion of convexity for subsets ofn-dimensional space. Many properties of convex sets can be discovered using just the linear structure. However, for more interesting results, it is necessary to introduce the notion of distance in order to discuss open sets, closed sets, bounded sets, and compact sets. The book illustrates the interplay between these linear and topological concepts, which makes the notion of convexity so interesting.Thoroughly class-tested, the book discusses topology and convexity in the context of normed linear spaces, specifically with a norm topology on ann-dimensional space.Geometry of Convex Setsalso features:An introduction ton-dimensional geometry including points; lines; vectors; distance; norms; inner products; orthogonality; convexity; hyperplanes; and linear functionalsCoverage ofn-dimensional norm topology including interior points and open sets; accumulation points and closed sets; boundary points and closed sets; compact subsets ofn-dimensional space; completeness ofn-dimensional space; sequences; equivalent norms; distance between sets; and support hyperplanes ·Basic properties of convex sets; convex hulls; interior and closure of convex sets; closed convex hulls; accessibility lemma; regularity of convex sets; affine hulls; flats or affine subspaces; affine basis theorem; separation theorems; extreme points of convex sets; supporting hyperplanes and extreme points; existence of extreme points; Krein–Milman theorem; polyhedral sets and polytopes; and Birkhoff’s theorem on doubly stochastic matricesDiscussions of Helly’s theorem; the Art Gallery theorem; Vincensini’s problem; Hadwiger’s theorems; theorems of Radon and Caratheodory; Kirchberger’s theorem;