This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of 2 or 3 dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution to different problems in these spaces. 1957 edition.
The following definition of convexity is used in this book. A subset X of R2 or R3 is convex if whenever x and y are in X the segment connecting them is also in X. Using this definition, a series of problems are presented and solved. Organized by chapter, they are Chapter 1) Problems in which convexity is used either by analogy or for subsidiary arguments *) The intersection of connected open sets *) Approximations … more