Ulam's conjecture on invariance of measure in the Hilbert cube / Soon-Mo Jung.
2023
QA322.4
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Title
Ulam's conjecture on invariance of measure in the Hilbert cube / Soon-Mo Jung.
Author
ISBN
9783031308864 (electronic bk.)
3031308867 (electronic bk.)
9783031308857
3031308859
3031308867 (electronic bk.)
9783031308857
3031308859
Published
Cham : Birkhũser, 2023.
Language
English
Description
1 online resource (x, 190 pages) : illustrations.
Item Number
10.1007/978-3-031-30886-4 doi
Call Number
QA322.4
Dewey Decimal Classification
515/.733
Summary
This book discusses the process by which Ulam's conjecture is proved, aptly detailing how mathematical problems may be solved by systematically combining interdisciplinary theories. It presents the state-of-the-art of various research topics and methodologies in mathematics, and mathematical analysis by presenting the latest research in emerging research areas, providing motivation for further studies. The book also explores the theory of extending the domain of local isometries by introducing a generalized span. For the reader, working knowledge of topology, linear algebra, and Hilbert space theory, is essential. The basic theories of these fields are gently and logically introduced. The content of each chapter provides the necessary building blocks to understanding the proof of Ulam's conjecture and are summarized as follows: Chapter 1 presents the basic concepts and theorems of general topology. In Chapter 2, essential concepts and theorems in vector space, normed space, Banach space, inner product space, and Hilbert space, are introduced. Chapter 3 gives a presentation on the basics of measure theory. In Chapter 4, the properties of first- and second-order generalized spans are defined, examined, and applied to the study of the extension of isometries. Chapter 5 includes a summary of published literature on Ulam?s conjecture; the conjecture is fully proved in Chapter 6.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 5, 2023).
Series
Frontiers in mathematics.
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Table of Contents
Preface
1. Topology
2. Hilbert spaces
3. Measure theory
4. Extension of isometries
5. History of Ulam?s conjecture
6. Ulam's conjecture. - Bibliography
Index.
1. Topology
2. Hilbert spaces
3. Measure theory
4. Extension of isometries
5. History of Ulam?s conjecture
6. Ulam's conjecture. - Bibliography
Index.