search for books and compare prices
Tables of Contents for Topology; A First Course
Chapter/Section Title
Page #
Page Count
Preface
xi
4
A Note to the Reader
xv
PART I
1
226
Chapter 1. Set Theory and Logic
3
72
1-1 Fundamental Concepts
4
11
1-2 Functions
15
6
1-3 Relations
21
8
1-4 The Integers and the Real Numbers
29
7
1-5 Arbitrary Cartesian Products
36
3
1-6 Finite Sets
39
6
1-7 Countable and Uncountable Sets
45
8
*1-8 The Principle of Recursive Definition
53
4
1-9 Infinite Sets and the Axiom of Choice
57
6
1-10 Well-Ordered Sets
63
5
*1-11 The Maximum Principle
68
4
*Supplementary Exercises: Well-Ordering
72
3
Chapter 2. Topological Spaces and Continuous Functions
75
71
2-1 Topological Spaces
75
3
2-2 Basis for a Topology
78
6
2-3 The Order Topology
84
2
2-4 The Product Topology on X x Y
86
3
2-5 The Subspace Topology
89
3
2-6 Closed Sets and Limit Points
92
9
2-7 Continuous Functions
101
11
2-8 The Product Topology
112
5
2-9 The Metric Topology
117
9
2-10 The Metric Topology (continued)
126
8
*2-11 The Quotient Topology
134
10
*Supplementary Exercises: Topological Groups
144
2
Chapter 3. Connectedness and Compactness
146
43
3-1 Connected Spaces
147
5
3-2 Connected Sets in the Real Line
152
7
*3-3 Components and Path Components
159
2
*3-4 Local Connectedness
161
3
3-5 Compact Spaces
164
9
3-6 Compact Sets in the Real Line
173
5
3-7 Limit Point Compactness
178
4
*3-8 Local Compactness
182
5
*Supplementary Exercises: Nets
187
2
Chapter 4. Countability and Separation Axioms
189
38
4-1 The Countability Axioms
190
5
4-2 The Separation Axioms
195
12
4-3 The Urysohn Lemma
207
9
4-4 The Urysohn Metrization Theorem
216
6
*4-5 Partitions of Unity
222
3
*Supplementary Exercises: Review of Part I
225
2
PART II
227
172
Chapter 5. The Tychonoff Theorem
229
15
5-1 The Tychonoff Theorem
229
6
5-2 Completely Regular Spaces
235
3
5-3 The Stone-Cech Compactification
238
6
Chapter 6. Metrization Theorems and Paracompactness
244
18
6-1 Local Finiteness
245
2
6-2 The Nagata-Smirnov Metrization Theorem (sufficiency)
247
4
6-3 The Nagata-Smirnov Theorem (necessity)
251
3
6-4 Paracompactness
254
6
6-5 The Smirnov Metrization Theorem
260
2
Chapter 7. Complete Metric Spaces and Function Spaces
262
54
7-1 Complete Metric Spaces
263
8
7-2 A Space-Filling Curve
271
3
7-3 Compactness in Metric Spaces
274
6
7-4 Pointwise and Compact Convergence
280
5
7-5 The Compact-Open Topology
285
4
7-6 Ascoli's Theorem
289
4
7-7 Baire Spaces
293
4
7-8 A Nowhere-Differentiable Function
297
4
7-9 An Introduction to Dimension Theory
301
15
Chapter 8. The Fundamental Group and Covering Spaces
316
83
8-1 Homotopy of Paths
318
8
8-2 The Fundamental Group
326
5
8-3 Covering Spaces
331
5
8-4 The Fundamental Group of the Circle
336
7
8-5 The Fundamental Group of the Punctured Plane
343
5
8-6 The Fundamental Group of S^n
348
3
8-7 Fundamental Groups of Surfaces
351
6
8-8 Essential and Inessential Maps
357
4
8-9 The Fundamental Theorem of Algebra
361
3
8-10 Vector Fields and Fixed Points
364
5
8-11 Homotopy Type
369
5
8-12 The Jordan Separation Theorem
374
4
8-13 The Jordan Curve Theorem
378
9
8-14 The Classification of Covering Spaces
387
12
Bibliography
399
2
Index
401