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商品の説明
内容説明
The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds.
The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed.
One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.
The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed.
One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.
Book Description
Hardbound. The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds.
The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed.
One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: <
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Excellent reference for Hilbert cube topology
2008/1/28
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The main reason I was interested in this book is one of the applications of chapter 8. My area of study is continuum theory and one of the most famous results is the Curtis-Schori-West Hyperspace theorem that states that the hyperspace of compacta of a continuum is homeomorphic to the Hilbert cube when the continuum is locally connected. However, this result uses techniques of infinite dimensional topology. That is the reason I wanted to read this book, to learn all the necessary background to the proof. Of course I learned even more than I needed and got an awesome new perspective on this subject. I don't know anything else about the subject so I cannot know if there is anything that this book lacks in content. However, at least for the beginner (like me) this book is definitely a good recommendation.
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