Topology : point-set and geometric /

Topology : point-set and geometric /

This text covers the essentials of point-set topology in a relatively terse presentation, with lots of examples and motivation along the way. Along with the standard point-set topology topics (connected spaces, compact spaces, separation axioms, and metric spaces), the author includes path-connected...

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Bibliographic Details
Main Author: Shick, Paul Louis, 1956-
Format: eBook
Language:English
Published: Hoboken, N.J. : Wiley-Interscience, ©2007.
Series:Pure and applied mathematics (John Wiley & Sons : Unnumbered)
Subjects:
Algebraic topology.
Point set theory.
Online Access:CONNECT
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Table of Contents:
  • Front Matter
  • Introduction: Intuitive Topology
  • Background on Sets and Functions
  • Topological Spaces
  • More on Open and Closed Sets and Continuous Functions
  • New Spaces from Old
  • Connected Spaces
  • Compact Spaces
  • Separation Axioms
  • Metric Spaces
  • The Classification of Surfaces
  • Fundamental Groups and Covering Spaces
  • References
  • Index
  • Pure and Applied Mathematics.
  • foreword
  • Acknowledgments
  • 1. Introduction : Intuitive topology
  • 1.1. Introduction : intuitive topology
  • 2. Background on sets and functions
  • 2.1. Sets
  • 2.2. Functions
  • 2.3. Equivalence relations
  • 2.4. Induction
  • 2.5. Cardinal numbers
  • 2.6. Groups
  • 3. Topological spaces
  • 3.1. Introduction
  • 3.2. Definitions and examples
  • 3.3. Basics on open and closed sets
  • 3.4. The subspace topology
  • 3.5. Continuous functions
  • 4. More on open and closed sets and continuous functions
  • 4.1. Introduction
  • 4.2. Basis for a topology
  • 4.3. Limit points
  • 4.4. Interior, boundary and closure
  • 4.5. More on continuity
  • 5. New spaces from old
  • 5.1. Introduction
  • 5.2. Product spaces
  • 5.3. Infinite product spaces (optional)
  • 5.4. Quotient spaces
  • 5.5. Unions and wedges
  • 6. Connected spaces
  • 6.1. Introduction
  • 6.2. Definition, examples and properties
  • 6.3. Connectedness in the real line
  • 6.4. Path-connectedness
  • 6.5. Connectedness of unions and finite products
  • 6.6. Connnectedness of infinite products (optional)
  • 7. Compact spaces
  • 7.1. Introduction
  • 7.2. Definition, examples and properties
  • 7.3. Hausdorff spaces and compactness
  • 7.4. Compactness in the real line
  • 7.5. Compactness of products
  • 7.6. Finite intersection property (optional).
  • 8. Separation axioms
  • 8.1. Introduction
  • 8.2. Definition and examples
  • 8.3. Regular and normal spaces
  • 8.4. Separation axioms and compactness
  • 9. Metric spaces
  • 9.1. Introduction
  • 9.2. Definition and examples
  • 9.3. Properties of metric spaces
  • 9.4. Basics on sequences
  • 10. The classification of surfaces
  • 10.1. Introduction
  • 10.2. Surfaces and higher-dimensional manifolds
  • 10.3. Connected sums of surfaces
  • 10.4. The classification theorem
  • 10.5. Triangulations of surfaces
  • 10.6. Proof of the classification theorem
  • 10.7. Euler characteristics and uniqueness
  • 11. Fundamental groups and covering spaces
  • 11. 1. Introduction
  • 11.2. Homotopy of functions and paths
  • 11.3. An operation on paths
  • 11.4. The fundamental group
  • 11.5. Covering spaces
  • 11.6. Fundamental group of the circle and related spaces
  • 11.7. The fundamental groups of surfaces
  • References
  • Index.

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