# 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...

Full description

Saved in:
Main Author: eBook English Hoboken, N.J. : Wiley-Interscience, ©2007. Pure and applied mathematics (John Wiley & Sons : Unnumbered) CONNECT CONNECT
• 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.