Elementary Topology

Dennis Roseman (Autor)

Buch | Hardcover

400 Seiten

1999
Pearson (Verlag)
978-0-13-863879-5 (ISBN)

Infos

Offering an introduction to topics of topology, this book is designed both for students who take only one course in topology and for those who are preparing for advanced work. It provides concrete examples, and guidance for building reasoning skills and writing proofs.

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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.

Inhalt

   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 Poincaré 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.

Produkt-Details

• Erscheint lt. Verlag: 29.6.1999
• Sprache: englisch
• Maße: 236 x 160 mm
• Gewicht: 708 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 0-13-863879-9 / 0138638799
• ISBN-13: 978-0-13-863879-5 / 9780138638795
• Zustand: Neuware