Elements of topology / Tej Bahadur Singh.

Format:

Book

Author/Creator:

Singh, Tej Bahadur (Mathematician)

Contributor:

Phi Beta Kappa Library Trust Fund.

Language:

English

Subjects (All):

Topology.

Physical Description:

xxi, 530 pages : illustrations ; 25 cm

Place of Publication:

Boca Raton, FL : CRC Press, [2013]

Summary:

"Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems in geometry and numerous other areas of mathematics. Elements of Topology provides a basic introduction to point-set topology and algebraic topology. It is intended for advanced undergraduate and beginning graduate students with working knowledge of analysis and algebra. Topics discussed include the theory of convergence, function spaces, topological transformation groups, fundamental groups, and covering spaces. The author makes the subject accessible by providing more than 250 worked examples and counterexamples with applications. The text also includes numerous end-of-section exercises to put the material into context"-- Provided by publisher.

Contents:

1 Topological Spaces 1

1.1 Metric Spaces 1

1.2 Topologies 7

1.3 Derived Concepts 12

1.4 Bases 19

1.5 Subspaces 30

2 Continuity and Products 35

2.1 Continuity 35

2.2 Product Topology 45

3 Connectedness 63

3.1 Connected Spaces 63

3.2 Components 72

3.3 Path-connected Spaces 77

3.4 Local Connectivity 82

4 Convergence 93

4.1 Sequences 93

4.2 Nets 96

4.3 Filters 103

4.4 Hausdorff Spaces 106

5 Countability Axioms 113

5.1 1st and 2nd Countable Spaces 113

5.2 Separable and Lindelöf Spaces 119

6 Compactness 125

6.1 Compact Spaces 125

6.2 Countably Compact Spaces 136

6.3 Compact Metric Spaces 140

6.4 Locally Compact Spaces 148

6.5 Proper Maps 155

7 Topological Constructions 159

7.1 Quotient Spaces 159

7.2 Identification Maps 173

7.3 Cones, Suspensions and Joins 180

7.4 Wedge Sums and Smash Products 188

7.5 Adjunction Spaces 195

7.6 Coinduced and Coherent Topologies 202

8 Separation Axioms 211

8.1 Regular Spaces 211

8.2 Normal Spaces 216

8.3 Completely Regular Spaces 229

8.4 Stone-Cech Compactification 235

9 Paracompactness and Metrisability 241

9.1 Paracompact Spaces 241

9.2 A Metrisation Theorem 252

10 Completeness 257

10.1 Complete Spaces 257

10.2 Completion 265

10.3 Baire Spaces 269

11 Function Spaces 275

11.1 Topology of Pointwise Convergence 275

11.2 Compact-Open Topology 283

11.3 Topology of Compact Convergence 301

12 Topological Groups 313

12.1 Examples and Basic Properties 313

12.2 Subgroups 324

12.3 Isomorphisms 331

12.4 Direct Products 341

13 Transformation Groups 347

13.1 Group Actions 347

13.2 Orbit Spaces 365

14 The Fundamental Group 371

14.1 Homotopic Maps 371

14.2 The Fundamental Group 383

14.3 Fundamental Groups of Spheres 397

14.4 Some Group Theory 408

14.5 The Seifert-van Kampen Theorem 424

15 Covering Spaces 439

15.1 Covering Maps 439

15.2 The Lifting Problem 448

15.3 The Universal Covering Space 459

15.4 Deck Transformations 468

15.5 The Existence of Covering Spaces 480.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Phi Beta Kappa Library Trust Fund.

ISBN:

1439871957

9781439871959

OCLC:

769420427

Publisher Number:

99954909085