CONTENTS Abstract v 1. Problems, Methods, and Main Results 1 PART I. PRELIMINARIES 2. Brouwerian Counterexamples 7 3. Real Numbers 13 4. Infima and Suprema 21 5. Metric Spaces 29 PART II. RELIEFS AND CONTINUOUS FUNCTIONS 6. Reliefs 35 7. Continuity 49 8. Intermediate Values 57 9. Bounds and Extremes 61 10. Connectivity and Convexity 65 11. Located Sets 71 PART III. MONOTONE FUNCTIONS 12. Monotonicity 75 13. Monotonicity and Continuity 81 PART IV. RELIEF FUNCTIONS AND THE LIMITED CONTINUITY PRINCIPLE 14. Relief Functions 85 15. Existence of Relief Functions 97 16. The Limited Continuity Principle 103 References 111 Index of Symbols 113 Index of Terms 115 iii
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