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Topology of Infinite-Dimen
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Item specifics
- Condition
- ISBN-13
- 9789811575778
- Book Title
- Topology of Infinite-Dimensional Manifolds
- ISBN
- 9789811575778
- Subject Area
- Mathematics
- Publication Name
- Topology of Infinite-Dimensional Manifolds
- Publisher
- Springer
- Item Length
- 9.3 in
- Subject
- Functional Analysis, Geometry / General, Topology
- Publication Year
- 2021
- Series
- Springer Monographs in Mathematics Ser.
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Weight
- 33.9 Oz
- Item Width
- 6.1 in
- Number of Pages
- Xv, 619 Pages
About this product
Product Identifiers
Publisher
Springer
ISBN-10
9811575770
ISBN-13
9789811575778
eBay Product ID (ePID)
25057275675
Product Key Features
Number of Pages
Xv, 619 Pages
Publication Name
Topology of Infinite-Dimensional Manifolds
Language
English
Subject
Functional Analysis, Geometry / General, Topology
Publication Year
2021
Type
Textbook
Subject Area
Mathematics
Series
Springer Monographs in Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Weight
33.9 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Reviews
"This is an excellent textbook for graduate students and researchers in infinite-dimensional topology, geometric topology, and general topology, as well as other branches related to topology and its applications. It can also be used as a good reference book." (Sergey A. Antonyan, Mathematical Reviews, September, 2022) "This is an extraordinary piece of mathematical literature. As a reviewer, I have tried to incorporate as much of the important material as I could, but surely I was not able to cover all the ground that has laid bare in this work even though I spent many hours on it." (Leonard R. Rubin, zbMATH 1481.57002, 2022), "This is an extraordinary piece of mathematical literature. As a reviewer, I have tried to incorporate as much of the important material as I could, but surely I was not able to cover all the ground that has laid bare in this work even though I spent many hours on it." (Leonard R. Rubin, zbMATH 1481.57002, 2022)
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
Chapter 1: Preliminaries and Background Results.- Chapter 2: Fundamental Results on Infinite-Dimensional Manifolds.- Chapter 3: Characterizations of Hilbert Manifolds and Hilbert Cube Manifolds.- Chapter 4: Triangulation of Hilbert Cube Manifolds and Related Topics.- Chapter 5: Manifolds Modeled on Homotopy Dense Subspaces of Hilbert Spaces.- Chapter 6: Manifolds Modeled on Direct Limits and Combinatorial Manifold.- Appendex: PL n-Manifolds and Combinatorial n-Manifolds.- Epilogue.- Bibliography.- Index.
Synopsis
An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book. Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk's conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial ∞-manifolds, the infinite-dimensional version of combinatorial n -manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial ∞-manifold and the Hauptvermutung for them is true., An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book. Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk's conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial -manifolds, the infinite-dimensional version of combinatorial n -manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial -manifold and the Hauptvermutung for them is true.
LC Classification Number
QA613-613.8
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