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Author: Thomas A. Chapman
Publisher:
ISBN:
Category :
Languages : en
Pages : 106
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Book Description
Author: Thomas A. Chapman
Publisher:
ISBN:
Category :
Languages : en
Pages : 106
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Book Description
Author: Thomas A. Chapman
Publisher: American Mathematical Soc.
ISBN: 0821816780
Category : Mathematics
Languages : en
Pages : 145
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Book Description
The goal of these lectures is to present an introduction to the geometric topology of the Hilbert cube Q and separable metric manifolds modeled on Q, which are called here Hilbert cube manifolds or Q-manifolds. In the past ten years there has been a great deal of research on Q and Q-manifolds which is scattered throughout several papers in the literature. The author presents here a self-contained treatment of only a few of these results in the hope that it will stimulate further interest in this area. No new material is presented here and no attempt has been made to be complete. For example, the author has omitted the important theorem of Schori-West stating that the hyperspace of closed subsets of $[0,1]$ is homeomorphic to Q.In an appendix (prepared independently by R. D. Anderson, D. W. Curtis, R. Schori and G. Kozlowski) there is a list of problems which are of current interest. This includes problems on Q-manifolds as well as manifolds modeled on various linear spaces. The reader is referred to this for a much broader perspective of the field. In the first four chapters, the basic tools which are needed in all of the remaining chapters are presented. Beyond this there seem to be at least two possible courses of action. The reader who is interested only in the triangulation and classification of Q-manifolds should read straight through (avoiding only Chapter VI). In particular the topological invariance of Whitehead torsion appears in Section 38. The reader who is interested in R. D. Edwards' recent proof that every ANR is a Q-manifold factor should read the first four chapters and then (with the single exception of 26.1) skip over to Chapters XIII and XIV.
Author: Katsuro Sakai
Publisher: Springer Nature
ISBN: 9811575754
Category : Mathematics
Languages : en
Pages : 619
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Book Description
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.
Author: Terry L. Lay
Publisher:
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 140
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Author: Alan Kenneth Jones
Publisher:
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 156
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Author: Henryk Toruńczyk
Publisher: American Mathematical Soc.
ISBN: 9780821824719
Category : Mathematics
Languages : en
Pages : 75
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: William O. Nowell
Publisher:
ISBN:
Category : Hilbert space
Languages : en
Pages : 124
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Book Description
Author: Leon Stagg Newman
Publisher:
ISBN:
Category : Embedding theorems
Languages : en
Pages : 148
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Book Description
Author: Bruce Hughes
Publisher: Cambridge University Press
ISBN: 0521576253
Category : Mathematics
Languages : en
Pages : 384
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Book Description
A systematic exposition of the theory and practice of ends of manifolds and CW complexes, not previously available.
