Infinite-Dimensional Topology. Prerequisites and Introduction (North-Holland Mathematical Library Volume 43) 1st Edition by J. van Mill (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review …recommended to anyone who wishes to get familiar with infinite-dimensional topology and at the same time learn about some its most beautiful results.Zentralblatt für Mathematik

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐It’s very good.

⭐It is a used book but I was aware of it. It is in a good condition

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