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Infinite-Dimensional Topology, Volume 43 - Prerequisites and Introduction (Hardcover)
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Infinite-Dimensional Topology, Volume 43 - Prerequisites and Introduction (Hardcover)
Series: North-Holland Mathematical Library
Expected to ship within 12 - 17 working days
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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.
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