1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X}, X2, '," xn)j Ixl is the length of n n a vector x E lR. and (x, y) is the scalar product of vectors x and y in lR., i.e., for x = (Xl, X2, ., xn) and y = (y}, Y2, ..., Yn), Ixl = Jx + x + ... + x, (x, y) = XIYl + X2Y2 + ... + XnYn. n Given arbitrary points a and b in lR., we denote by a, b] the segment that joins n them, i.e. the collection of points x E lR. of the form x = >.a + I'b, where>. + I' = 1 and >. 0, I' O. n We...