Author: | J. van Mill |

Publisher | Elsevier (North-Holland) |

Series: | North-Holland Mathematical Library, 43 |

Year: | 1989 |

Review: | AMS review |

- Extension Theorems

Topological Spaces. Linear Spaces. Function Spaces. The Michael Selection Theorem and Applications. AR's and ANR's. The Borsuk Homotopy Extension Theorem.

- Elementary Plane Topology.

The Brouwer Fixed-Point Theorem and Applications. The Borsuk-Ulam Theorem. The Poincaré Theorem. The Jordan Curve Theorem.

- Elementary Combinatorial Techniques.

Affine Notions. Simplexes. Triangulation. Simplexes in Rn. The Brouwer Fixed-Point Theorem. Topologizing a Simplical Complex.

- 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.

- Elementary ANR Theory.

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.

- An Introduction to Infinite-Dimensional Topology.

Constructing New Homeomorphisms from Old. Z-Sets. The Estimated Homeomorphism Extension Theorem for Compacta in s. The Estimated HomeomorphismExtension Theorem. Absorbers. Hilbert Space is Homeomorphic to the Countable Infinite Product of Lines. Inverse Limits. Hilbert Cube Factors.

- 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. Torunczyk's Approximation Theorem and Applications. Cell-Like Maps. The Characterization Theorem.

- Applications. Infinite Products.

Keller's Theorem. Cone Characterization of the Hilbert Cube. The Curtis-Schori-West Hyperspace Theorem.

Bibliography

Subject Index