Real Analysis : With Basic Metric Space Topology

ISBN-10: 078030408X
ISBN-13: 9780780304086
Edition: N/A
Authors: Robert Ash
List price: $79.95
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Book details

List price: $79.95
Publisher: IEEE
Binding: Hardcover
Pages: 232
Size: 6.50" wide x 9.50" long x 0.75" tall
Weight: 1.100
Language: English

Preface
How to Write Mathematics for Nonmathematicians and Mathematicians Alike
Introductionp. 1
Basic Terminologyp. 1
Finite and Infinite Sets; Countably Infinite and Uncountably Infinite Setsp. 7
Distance and Convergencep. 10
Minicourse in Basic Logicp. 15
Limit Points and Closurep. 21
Review Problems for Chapter 1p. 23
Some Basic Topological Properties of [actual symbols not reproducible]p. 25
Unions and Intersections of Open and Closed Setsp. 25
Compactnessp. 28
Some Applications of Compactnessp. 33
Least Upper Bounds and Completenessp. 37
Review Problems for Chapter 2p. 42
Upper and Lower Limits of Sequences of Real Numbersp. 45
Generalization of the Limit Conceptp. 45
Some Properties of Upper and Lower Limitsp. 49
Convergence of Power Seriesp. 52
Review Problems for Chapter 3p. 56
Continuous Functionsp. 57
Continuity: Ideas, Basic Terminology, Propertiesp. 57
Continuity and Compactnessp. 64
Types of Discontinuitiesp. 70
The Cantor Setp. 76
Review Problems for Chapter 4p. 80
Differentiationp. 81
The Derivative and Its Basic Propertiesp. 81
Additional Properties of the Derivative; Some Applications of the Mean Value Theoremp. 86
Review Problems for Chapter 5p. 92
Riemann-Stieltjes Integrationp. 93
Definition of the Integralp. 93
Properties of the Integralp. 98
Functions of Bounded Variationp. 106
Some Useful Integration Theoremsp. 111
Review Problems for Chapter 6p. 115
Uniform Convergence and Applicationsp. 117
Pointwise and Uniform Convergencep. 117
Uniform Convergence and Limit Operationsp. 122
The Weierstrass M-test and Applicationsp. 125
Equicontinuity and the Arzela-Ascoli Theoremp. 130
The Weierstrass Approximation Theoremp. 134
Review Problems for Chapter 7p. 139
Further Topological Resultsp. 141
The Extension Problemp. 141
Baire Category Theoremp. 144
Connectednessp. 150
Semicontinuous Functionsp. 152
Review Problems for Chapter 8p. 158
Epiloguep. 161
Some Compactness Resultsp. 161
Replacing Cantor's Nested Set Propertyp. 164
The Real Numbers Revisitedp. 165
Solutions to Problemsp. 167
Indexp. 207
Table of Contents provided by Blackwell. All Rights Reserved.

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