[PDF] Modern Analysis And Topology eBook

Author : Norman R. Howes
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 28,93 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461208335

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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 : Albert Wilansky
Publisher : Courier Corporation
Page : 399 pages
File Size : 30,42 MB
Release : 2008-10-17
Category : Mathematics
ISBN : 0486469034

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Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.

Author : George Finlay Simmons
Publisher : Ingram
Page : 372 pages
File Size : 15,56 MB
Release : 1963
Category : Mathematics
ISBN : 9781575242385

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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 : Avner Friedman
Publisher : Courier Corporation
Page : 276 pages
File Size : 24,68 MB
Release : 1982-01-01
Category : Mathematics
ISBN : 9780486640624

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Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

Author : Tai-Danae Bradley
Publisher : MIT Press
Page : 167 pages
File Size : 17,29 MB
Release : 2020-08-18
Category : Mathematics
ISBN : 0262359626

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A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Author : Gerald B. Folland
Publisher : John Wiley & Sons
Page : 368 pages
File Size : 48,73 MB
Release : 2013-06-11
Category : Mathematics
ISBN : 1118626397

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An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.

Author : Paul Alexandroff
Publisher : Courier Corporation
Page : 68 pages
File Size : 10,91 MB
Release : 2012-08-13
Category : Mathematics
ISBN : 0486155064

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Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Author : Nikolaos Katzourakis
Publisher : CRC Press
Page : 558 pages
File Size : 16,83 MB
Release : 2018-01-02
Category : Mathematics
ISBN : 1351765337

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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 : Z. Frolík
Publisher : Academic Press
Page : 366 pages
File Size : 37,51 MB
Release : 2014-05-12
Category : Mathematics
ISBN : 1483223531

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General Topology and Its Relations to Modern Analysis and Algebra II is comprised of papers presented at the Second Symposium on General Topology and its Relations to Modern Analysis and Algebra, held in Prague in September 1966. The book contains expositions and lectures that discuss various subject matters in the field of General Topology. The topics considered include the algebraic structure for a topology; the projection spectrum and its limit space; some special methods of homeomorphism theory in infinite-dimensional topology; types of ultrafilters on countable sets; the compactness operator in general topology; and the algebraic generalization of the topological theorems of Bolzano and Weierstrass. This publication will be found useful by all specialists in the field of Topology and mathematicians interested in General Topology.