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This title in other editionsReal Variables with Basic Metric Space Topologyby Robert B. Ash
Synopses & ReviewsSynopsis:Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition. Synopsis:Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition. Table of ContentsINTRODUCTION Basic Terminology Finite and Infinite Sets; Countably Infinite and Uncountably Infinite Sets Distance and Convergence Minicourse in Basic Logic Limit Points and Closure Review Problems for Chapter 1 SOME BASIC TOPOLOGICAL PROPERTIES OF Rp Unions and Intersections of Open and Closed Sets Compactness Some Applications of Compactness Least Upper Bounds and Completeness Review Problems for Chapter 2 UPPER AND LOWER LIMITS OF SEQUENCES OF REAL NUMBERS Generalization of the Limit Concept Some Properties of Upper and Lower Limits Convergence of Power Series Review Problems for Chapter 3 CONTINUOUS FUNCTIONS Continuity: Ideas, Basic Terminology, Properties Continuity and Compactness Types of Discontinuities The Cantor Set Review Problems for Chapter 4 DIFFERENTIATION The Derivative and Its Basic Properties Additional Properties of the Derivative; Some Applications of the Mean Value Theorem Review Problems for Chapter 5 RIEMANNSTIELTJES INTEGRATION Definition of the Integral Properties of the Integral Functions of Bounded Variation Some Useful Integration Theorems Review Problems for Chapter 6 UNIFORM CONVERGENCE AND APPLICATIONS Pointwise and Uniform Convergence Uniform Convergence and Limit Operations The Weierstrass Mtest and Applications Equicontinuity and the ArzelaAscoli Theorem The Weierstrass Approximation Theorem Review Problems for Chapter 7 FURTHER TOPOLOGICAL RESULTS The Extension Problem Baire Category Theorem Connectedness Semicontinuous Functions Review Problems for Chapter 8 EPILOGUE Some Compactness Results Replacing Cantor's Nested Set Property The Real Numbers Revisited SOLUTIONS TO PROBLEMS INDEX What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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