Modern Analysis: Topology of Metric Spaces PDF Download
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Author: Sudhir Kumar Pundir
Publisher:
ISBN: 9789354660108
Category : Mathematics
Languages : en
Pages : 412
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Book Description
An introductory text aimed at graduate and postgraduate students of mathematics.
Author: Sudhir Kumar Pundir
Publisher:
ISBN: 9789354660108
Category : Mathematics
Languages : en
Pages : 412
Get Book
Book Description
An introductory text aimed at graduate and postgraduate students of mathematics.
Author: S. Kumaresan
Publisher: Alpha Science Int'l Ltd.
ISBN: 9781842652503
Category : Computers
Languages : en
Pages : 172
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Book Description
"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.
Author: Norman R. Howes
Publisher: Springer Science & Business Media
ISBN: 1461208335
Category : Mathematics
Languages : en
Pages : 434
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Book Description
The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be accessible to a reader of modest background. An advanced calculus course and an introductory topology course should be adequate. But it is also intended that this book be able to take the reader from that state to the frontiers of modern analysis and topology in-so-far as they can be done within the framework of uniform spaces. Modern analysis is usually developed in the setting of metric spaces although a great deal of harmonic analysis is done on topological groups and much offimctional analysis is done on various topological algebraic structures. All of these spaces are special cases of uniform spaces. Modern topology often involves spaces that are more general than uniform spaces, but the uniform spaces provide a setting general enough to investigate many of the most important ideas in modern topology, including the theories of Stone-Cech compactification, Hewitt Real-compactification and Tamano-Morita Para compactification, together with the theory of rings of continuous functions, while at the same time retaining a structure rich enough to support modern analysis.
Author: George Finlay Simmons
Publisher: Ingram
ISBN: 9781575242385
Category : Mathematics
Languages : en
Pages : 372
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Book Description
This material is intended to contribute to a wider appreciation of the mathematical words "continuity and linearity". The book's purpose is to illuminate the meanings of these words and their relation to each other --- Product Description.
Author: Nikolaos Katzourakis
Publisher: CRC Press
ISBN: 1351765337
Category : Mathematics
Languages : en
Pages : 558
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Book Description
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.
Author: William P. Ziemer
Publisher: Springer
ISBN: 331964629X
Category : Mathematics
Languages : en
Pages : 382
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Book Description
This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations. This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.
Author: Satish Shirali
Publisher: Springer Science & Business Media
ISBN: 9781852339227
Category : Mathematics
Languages : en
Pages : 238
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Book Description
One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
Author: Simion Stoilow
Publisher: World Scientific
ISBN: 9789810227616
Category : Mathematics
Languages : en
Pages : 744
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Book Description
The goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology. It provides an attempt to study various approaches in the topological applications and influence to Function Theory, Calculus of Variations, Functional Analysis and Approximation Theory. The volume is dedicated to the memory of S Stoilow.
Author: George Finlay Simmons
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages : 392
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Book Description
Author: Avishek Adhikari
Publisher: Springer Nature
ISBN: 9811665095
Category : Mathematics
Languages : en
Pages : 523
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Book Description
This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
