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## Details

Genre/Form: | Textbooks |
---|---|

Document Type: | Book |

All Authors / Contributors: |
R D Bhatt |

ISBN: | 1842655140 9781842655146 |

OCLC Number: | 303020705 |

Description: | xii, 429 p. : ill. ; 25 cm. |

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. |

Responsibility: | R.D. Bhatt. |

### Abstract:

Aims at presenting advanced topics such as continuity, uniform continuity, tests of convergence of series, polynomial approximations and Fourier series in a more general setting. This book places a consistent emphasis on showing the power of the classical analysis by applying it to the study of real valued functions and their applications.
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