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A ProblemText in Advanced Calculus

A ProblemText in Advanced CalculusJohn M. ErdmanPortland State UniversityVersion July 1, 2014E-mail ArgentinaContentsPREFACExiFOR STUDENTS: HOW TO USE THIS PROBLEMTEXTxvChapter 1. DISTANCE AND INTERIOR OF A SET2 Chapter 2. TOPOLOGY OF THE REAL OPEN SUBSETS CLOSED SUBSETS OFR7 Chapter 3. CONTINUOUS FUNCTIONS CONTINUITY AS A LOCAL CONTINUITY AS A GLOBAL FUNCTIONS DEFINED ON SUBSETS OFR13 Chapter 4. SEQUENCES OF REAL CONVERGENCE OF ALGEBRAIC COMBINATIONS OF SUFFICIENT CONDITION FOR SUBSEQUENCES23 Chapter 5. CONNECTEDNESS AND THE INTERMEDIATE VALUE CONNECTED SUBSETS CONTINUOUS IMAGES OF CONNECTED HOMEOMORPHISMS30 Chapter 6. COMPACTNESS AND THE EXTREME VALUE EXAMPLES OF COMPACT SUBSETS THE EXTREME VALUE THEOREM36 Chapter 7.

an integrated overview of Calculus and, for those who continue, a solid foundation for a rst year graduate course in Real Analysis. As the title of the present document, ProblemText in Advanced Calculus, is intended to suggest, it is as much an extended problem set as a textbook. The proofs of most of the major results are either exercises or ...

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