Book:Gerard Buskes/Topological Systems: From Distance to Neighborhood
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Gerard Buskes and Arnoud van Rooij: Topological Systems: From Distance to Neighborhood
Published $\text {1997}$, Springer-Verlag New York, Inc.
- ISBN 0-387-94994-1
Subject Matter
Contents
- Preface
- PART I. THE LINE AND THE PLANE
- Chapter 1. What Topology Is About
- Topological Equivalence
- Continuity and Convergence
- A Few Conventions
- Extra: Topological Diversions
- Exercises
- Chapter 2. Axioms for $\R$
- Extra: Axiom Systems
- Exercises
- Chapter 3. Convergent Sequences and Continuity
- Subsequences
- Uniform Continuity
- The Plane
- Extra: Bolzano (1781-1848)
- Exercises
- Chapter 4. Curves in the Plane
- Curves
- Homeomorphic Sets
- Brouwer's Theorem
- Extra: L.E.J. Brouwer (1881-1966)
- PART II. METRIC SPACES
- Chapter 5. Metrics
- Extra: Camille Jordan (1838-1922)
- Exercises
- Chapter 6. Open and Closed Sets
- Subsets of a Metric Space
- Collections of Sets
- Similar Metrics
- Interior and Closure
- The Empty Set
- Extra: Cantor (1845-1918)
- Chapter 7. Completeness
- Extra: Meager Sets and the Mazur Game
- Exercises
- Chapter 8. Uniform Convergence
- Extra: Spaces of Continuous Functions
- Exercises
- Chapter 9. Sequential Compactness
- Extra: The p-adic Numbers
- Exercises
- Chapter 10. Convergent Nets
- Inadequacy of Sequences
- Convergent Nets
- Extra: Knots
- Exercises
- Chapter 11. Transition to Topology
- Generalized Convergence
- Topologies
- Extra: The Emergence of the Professional Mathematician
- Exercises
- PART III. TOPOLOGICAL SPACES
- Chapter 12. Topological Spaces
- Extra: Map Coloring
- Exercises
- Chapter 13. Compactness and the Hausdorff Property
- Compact Spaces
- Hausdorff Spaces
- Extra: Hausdorff and the Measure Problem
- Exercises
- Chapter 14. Products and Quotients
- Product Spaces
- Quotient Spaces
- Extra: Surfaces
- Exercises
- Chapter 15. The Hahn-Tietze-Tong-Urysohn Theorems
- Urysohn's Lemma
- Interpolation and Extension
- Extra: Nonstandard Mathematics
- Exercises
- Chapter 16. Connectedness
- Connected Spaces
- The Jordan Theorem
- Extra: Continuous Deformation of Curves
- Exercises
- Chapter 17. Tychonoff's Theorem
- Extra: The Axiom of Choice
- Exercises
- PART IV. POSTSCRIPT
- Chapter 18. A Smorgasbord for Further Study
- Countability Conditions
- Separation Conditions
- Compactness Conditions
- Compactifications
- Connectivity Conditions
- Extra: Dates from the History of General Topology
- Exercises
- Chapter 19. Countable Sets
- Extra: The Continuum Hypothesis