Transcription of A ProblemText in Advanced Calculus
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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.
ground in all sorts of things: quanti ers, logical connectives, set operations, writing proofs, the arithmetic and order properties of the real numbers, mathematical induction, least upper bounds, functions, composition of functions, images and inverse images of sets under functions, nite and in nite sets, countable and uncountable sets.
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