First concepts of topology [[electronic resource] ] : the geometry of mappings of segments, curves, circles and disks / / by William G. Chinn and N.E. Steenrod

• Autore: Chinn William G
• Pubblicazione: Washington, D.C., : Mathematical Association of America, 1966
• Descrizione fisica: 1 online resource (169 p.)
• Disciplina: 514
• Soggetto topico: Topology; Geometry
• Soggetto genere / forma: Electronic books.
• Altri autori: SteenrodNorman Earl <1910-1971.>
• Note generali: Includes index.
• Nota di contenuto: ""Front Cover""; ""First Concepts of Topology: The Geometry of Mappings of Segments, Curves, Circles, and Disks""; ""Copyright Page""; ""Contents""; ""Introduction""; ""Part I: Existence Theorems in Dimension 1""; ""1. The first existence theorem""; ""2. Sets and functions""; ""3. Neighborhoods and continuity""; ""4. Open sets and closed sets""; ""5. The completeness of the real number system""; ""6. Compactness""; ""7. Connectedness""; ""8. Topological properties and topological equivalences""; ""9. A fixed point theorem""; ""10. Mappings of a circle into a line"" ; ""11. The pancake problems""""12. Zeros of polynomials""; ""Part II: Existence Theorems in Dimension 2""; ""13. Mappings of a plane into itself""; ""14. The disk""; ""15. Initial attempts to formulate the main theorem""; ""16. Curves and closed curves""; ""17. Intuitive definition of winding number""; ""18. Statement of the main theorem""; ""19. When is an argument not a proof?""; ""20. The angle swept out by a curve""; ""21. Partitioning a curve into short curves""; ""22. The winding number W(Ï?, γ)""; ""23. Properties of A(Ï?, γ) and W(Ï?, γ)""; ""24. Homotopies of curves"" ; ""25. Constancy of the winding number""""26. Proof of the main theorem""; ""27. The circle winds once about each interior point""; ""28. The fixed point property""; ""29. Vector fields""; ""30. The equivalence of vector fields and mappings""; ""31. The index of a vector field around a closed curve""; ""32. The mappings of a sphere into a plane""; ""33. Dividing a ham sandwich""; ""34. Vector fields tangent to a sphere""; ""35. Complex numbers""; ""36. Every polynomial has a zero""; ""37. Epilogue: A brief glance at higher dimensional cases""; ""Solutions for Exercises""; ""Index"" ; ""Back Cover""
• Sommario/riassunto: Over 150 problems and solutions.
• Titolo autorizzato: First concepts of topology
• ISBN: 0-88385-933-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910461904403321
• Lo trovi qui: Univ. Federico II
• Serie: Anneli Lax New Mathematical Library