E-Book (epub) Real Variables with Basic Metric Space Topology von Robert B. Ash
CHF 10.55 10.90
Download steht sofort bereit
Autorentext

A Professor Emeritus of Mathematics at the University of Illinois, Robert Ash is the author of three other Dover books: Basic Abstract Algebra, Basic Probability Theory, and Complex Variables and Information Theory.



Inhalt

INTRODUCTION
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
RIEMANN-STIELTJES 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 M-test and Applications
Equicontinuity and the Arzela-Ascoli 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
Titel
Real Variables with Basic Metric Space Topology
Autor
Robert B. Ash
EAN
0800759151493
ISBN
978-0-486-15149-6
Format
E-Book (epub)
Hersteller
Apa Publications
Herausgeber
Dover Publications
Veröffentlichung
28.07.2014
Digitaler Kopierschutz
Adobe-DRM
Anzahl Seiten
224
Jahr
2014
Untertitel
Englisch