First Course in Topology

Name: First Course in Topology | An Introduction to Mathematical Thinking
Brand: Dover Publications
Price: 21.99 EUR
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An Introduction to Mathematical Thinking

Robert A. Conover(Autor*in)

Dover Publications (Verlag)

Erschienen am 20. Februar 2014

471 Seiten

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Inhalt

Cover
Title Page
Copyright Page
Dedication
Preface
Introduction
Proofs in Mathematics: A Note to the Reader
Contents
Chapter 1. Sets and Functions
1. Sets
2. Notation
3. Operations on Sets
4. Functions
5. Composition of Functions
Chapter 2. Infinite Sets and Transfinite Numbers
1. Basic Ideas
2. Cardinal Numbers Larger than c
3. Ordinal Numbers
4. Ordinal Numbers Greater than O
5. The Countable Ordinals
6. Well-Ordering and the Principle of Transfinite Induction
Chapter 3. Some Familiar Topological Spaces and Basic Topological Concepts
1. The Topology on the Real Line
2. The Euclidean Plane E2 as a Topological Space
3. Some Familiar Subsets of R as Topological Spaces
4. The Order Topology
5. Sequences in Metric Spaces
6. Continuity
7. Homeomorphism
8. Topological Manifolds
Chapter 4. Topological Spaces and Basic Topological Concepts in General
1. Definition of a Topological Space
2. Examples
3. Continuity
4. Neighborhoods
5. Closed Sets and Closure
6. Basis for a Topology
7. Topology Generated by a Basis
8. Sub-Basis for a Topology
9. Subspaces
10. Continuity Again
Chapter 5. Product Spaces
1. The Product of Two Spaces
2. Finite Products
3. Infinite Products
Chapter 6. Connectivity
1. Definition of Connectivity and Some Useful Consequences
2. Preservation of Connectivity by Certain Operations and Functions
3. Components and Local Connectivity
4. Other Kinds of Connectivity
Chapter 7. Compactness
1. The Definition of Compactness
2. Preservation of Compactness by Certain Operations and Functions and Some Consequences.
3. Some Equivalences of Compactness in R
4. Variations of Compactness
5. Uniform Conformity
Chapter 8. Separation Axioms
1. Weak Spaces
2. Hausdorff Spaces
3. Regular and Completely Regular Spaces
4. Normal Spaces :
Chapter 9. Complete Spaces
1. Definition of Completeness and Some Consequences
2. Completeness and Compactness
3. The Baire Category Theorem and Some Applications
4. The Space C*(X)
5. The Completion of a Metric Space
6. Compactness in Metric Spaces
Chapter 10. Compactness Again
1. Nets and Filters
2. Ultrafilters
3. The Stone-Cech Compactification
Chapter 11. Selected Topics in Point-Set Topology
1. More on Metric Spaces
2. Metrizability
3. Quotient Spaces
Chapter 12. Homotopy and the Fundamental Group
1. Homotopy
2. The Fundamental Group
3. An Intuitive Look at the Fundamental Group of Some Familiar Spaces
4. Applications
Bibliography
Index

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