For a one-semester, advanced undergraduate level course in Introduction to Topology. Designed both for students who will take only one course in topology as well as for those who are preparing for more advanced work, this text offers a thorough introduction to the important topics of topology, a variety of interesting, concrete examples, and ample opportunity and guidance for building reasoning skills and writing proofs. It integrates students' background in calculus, analytic geometry and linear algebra throughout the presentation.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Maße
Höhe: 160 mm
Breite: 236 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-0-13-863879-5 (9780138638795)
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Schweitzer Klassifikation
Preface
I. BASIC TOPICS.
1. Open and Closed Subsets.
2. Building Open and Closed Subsets.
3. Continuity.
4. Homeomorphism.
5. Cantor Sets and Allied Topics.
6. Embeddings.
7. Connectivity .
8. Path Connectedness.
9. Closure and Limit Points.
10. Compactness.
11. Local Connectivity.
II. ADVANCED TOPICS
12. Space Filling Curves.
13. Manifolds.
14. Knots and Kottings.
15. Simple Connectivity.
16. Deformation Type.
17. Complexes.
18. Higher Dimensions.
19. The Poincare Conjecture.
III. APPENDICES.
Appendix A. Sets and Logic.
Appendix B. Numbers.
Appendix C. Cardinality of Sets.
Appendix D. Summary from Calculus.
Appendix E. Strategy in Proof.
Bibliography.
Index of Examples, Remarks, and Propositions.
Subject Index.
