Prerequisites and Introduction
- J. van Mill, Vrije Universiteit, Department of Mathematics and Computer Science, Amsterdam, The Netherlands
- Published: December 1988
- Imprint: NORTH-HOLLAND
- ISBN: 978-0-444-87133-6
...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
Table of Contents
1. Extension Theorems. Topological Spaces. Linear Spaces. Function Spaces. The Michael Selection Theorem and Applications. AR's and ANR's. The Borsuk Homotopy Extension Theorem.
2. Elementary Plane Topology. The Brouwer Fixed-Point Theorem and Applications. The Borsuk-Ulam Theorem. The Poincaré Theorem. The Jordan Curve Theorem.
3. Elementary Combinatorial Techniques. Affine Notions. Simplexes. Triangulation. Simplexes in Rn. The Brouwer Fixed-Point Theorem. Topologizing a Simplical Complex.
4. Elementary Dimension Theory. The Covering Dimension. Zero-Dimensional Spaces. Translation into Open Covers. The Imbedding Theorem. The Inductive Dimension Functions ind and Ind. Mappings into Spheres. Totally Disconnected Spaces. Various Kinds of Infinite-Dimensionality.5. Elementary ANR Theory. Some Properties of ANR's. A Characterization of ANR's and AR's. Hyperspaces and the AR-Property. Open Subspaces of ANR's. Characterization of Finite-Dimensional ANR's and AR's. Adjunction Spaces of Compact A(N)R's.
6. An Introduction to Infinite-Dimensional Topology. Constructing New Homeomorphisms from Old. Z-Sets. The Estimated Homeomorphism Extension Theorem for Compacta in s. The Estimated Homeomorphism Extension Theorem. Absorbers. Hilbert Space is Homeomorphic to the Countable Infinite Product of Lines. Inverse Limits. Hilbert Cube Factors.7. Cell-Like Maps and Q-Manifolds. Cell-Like Maps and Fine Homotopy Equivalences. Z-Sets in ANR's. The Disjoint-Cells Property. Z-Sets in Q-Manifolds. Toruńczyk's Approximation Theorem and Applications. Cell-Like Maps. The Characterization Theorem.
8. Applications. Infinite Products. Keller's Theorem. Cone Characterization of the Hilbert Cube. The Curtis-Schori-West Hyperspace Theorem.What Next? Bibliography. Subject Index.