By: Bhatt, R.DContributor(s): N.APublication details: 2009Subject(s): MathematicsDDC classification: 517.1 Summary: Table of Contents
Preface
Metric Spaces: Definition of a Metric Space
Some Examples
Euclidean Metric in Kn
Normed Spaces: Normed Spaces
The Sequence Space lp, p>1:
Topology of Metric Spaces: Topological Spaces
Topology of Metric Spaces
Equivalent Metrics
Subspaces
Sequences in Metric Spaces
Closure, Interior and Boundary
Complete Metric Spaces: The Cauchy Sequence
Subsequences
Contraction Mapping
Continuity: Continuity between Metric Spaces
Open Maps, Closed Maps
Uniform Continuity
Homeomorphism and Isometry
Discontinuities and All That
Connected Metric Spaces: Connected Metric Spaces
Application of Intermediate Value Theorem
Connected Components
Path Connected Spaces
Compact Metric Spaces: Compactness
Characterization of Compact Metric Spaces
Applications
Sequences and Series of Functions: Pointwise Convergence
Uniform Convergence
Power Series: Limit Superior and Limit Inferior
Power Series
The Circular Functions
The Exponential Function
Fourier Series: Orthogonal Functions
Fourier Sine and Cosine Series
Mean Square Convergence of Fourier Series
The Pointwise Convergence of Fourier Series
Appendixes
Bibliography
Index
Index of Symbols.
Preface
Metric Spaces: Definition of a Metric Space
Some Examples
Euclidean Metric in Kn
Normed Spaces: Normed Spaces
The Sequence Space lp, p>1:
Topology of Metric Spaces: Topological Spaces
Topology of Metric Spaces
Equivalent Metrics
Subspaces
Sequences in Metric Spaces
Closure, Interior and Boundary
Complete Metric Spaces: The Cauchy Sequence
Subsequences
Contraction Mapping
Continuity: Continuity between Metric Spaces
Open Maps, Closed Maps
Uniform Continuity
Homeomorphism and Isometry
Discontinuities and All That
Connected Metric Spaces: Connected Metric Spaces
Application of Intermediate Value Theorem
Connected Components
Path Connected Spaces
Compact Metric Spaces: Compactness
Characterization of Compact Metric Spaces
Applications
Sequences and Series of Functions: Pointwise Convergence
Uniform Convergence
Power Series: Limit Superior and Limit Inferior
Power Series
The Circular Functions
The Exponential Function
Fourier Series: Orthogonal Functions
Fourier Sine and Cosine Series
Mean Square Convergence of Fourier Series
The Pointwise Convergence of Fourier Series
Appendixes
Bibliography
Index
Index of Symbols.
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