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This title in other editions

Real Variables with Basic Metric Space Topology

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Real Variables with Basic Metric Space Topology Cover

 

Synopses & Reviews

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.

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 Contents

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

Product Details

ISBN:
9780486472201
Author:
Ash, Robert B.
Publisher:
Dover Publications
Author:
Mathematics
Subject:
General Mathematics
Subject:
Mathematical Analysis
Subject:
Topology - General
Subject:
Calculus
Subject:
Functions of real variables
Subject:
Metric spaces
Subject:
Topology
Subject:
Mathematics-Analysis General
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20090531
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Y
Pages:
224
Dimensions:
9.25 x 6.13 in 0.76 lb

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Related Subjects


» Science and Mathematics » Mathematics » Analysis General
» Science and Mathematics » Mathematics » Differential Equations
» Science and Mathematics » Mathematics » Probability and Statistics » General
» Science and Mathematics » Mathematics » Probability and Statistics » Statistics
» Science and Mathematics » Mathematics » Real Analysis
» Science and Mathematics » Mathematics » Topology
» Science and Mathematics » Physics » Acoustics

Real Variables with Basic Metric Space Topology New Trade Paper
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Product details 224 pages Dover Publications - English 9780486472201 Reviews:
"Synopsis" by ,
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" by ,
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.
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