Front Cover; The Bidual of C(X) I; Copyright Page; Table of Contents; PREFACE; PART I: BACKGROUND; CHAPTER 1. RIESZ SPACES; 1 Ordered vector spaces; 2 Riesz spaces; 3 Riesz subspaces and Riesz ideals; 4 Order convergence; 5 Order closure and bands; 6 Riesz homomorphisms; 7 Dedekind completeness; 8 Countability properties; 9 Riesz norms and Banach lattices; Exercises; CHAPTER 2. RIESZ SPACE DUALITY; 10 The space Eb of order bounded linear functionals; 11 E as ""predual"" of Eb; 12 The space EC of order continuous linear functions; 13 The canonical imbedding of E in Ebb

28 Equi-order-continuity29 Weak compactness; PART III: C (X) , C' (X) , C"" (X) : THE FRAMEWORK; CHAPTER 6. (C(X) ,X) -DUALITY; 30 The topology of simple convergence on C(X); 31 The duality between the norm closed Riesz ideals of C(X) and the closed (or open) subsets of X; 32 The duality between the MII-subspaces of C(X) and the upper semicontinuous decomposition of X; 33 The MII-homomorphisms of C(X); CHAPTER 7. (C(X) , C ' (X))-DUALITY; 34 The imbedding of X in C'(X); 35 Atomic and diffuse Radon measures; 36 The vague topology on C'(X); 37 Mapping duality; CHAPTER 8. C""(X)

38 The imbedding of C(X) in C""(X)39 Some simple sequence spaces; PART IV: THE STRUCTURE OF C""(X) : BEGINNINGS; CHAPTER 9: THE FUNDAMENTAL SUBSPACES OF C""(X); 40 C""(X)a and C""(X)d; 41 The basic bands and Co""(X); 42 The ""semicontinuous"" elements; 43 The Up-down-up theorem; 44 The subspace U(X) of universally integrable elements; 45 The subspaces s(X) and S(X); 46 Dedekind closures; 47 The Borel subspace Bo(X); 48 C(X)(1) and C(X)(2); CHAPTER 10. THE OPERATORS u AND l; 49 The operators u and l; 50 The operator d; 51 l-bands and u-bands; 52 Applications to general bands; CHAPTER 11. U(X)