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First concepts of topology [[electronic resource] ] : the geometry of mappings of segments, curves, circles and disks / / by William G. Chinn and N.E. Steenrod
| 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 |
| Pubbl/distr/stampa | Washington, D.C., : Mathematical Association of America, 1966 |
| Descrizione fisica | 1 online resource (169 p.) |
| Disciplina | 514 |
| Altri autori (Persone) | SteenrodNorman Earl <1910-1971.> |
| Collana | The Anneli Lax new mathematical library |
| Soggetto topico |
Topology
Geometry |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-88385-933-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910461904403321 |
Chinn William G
|
||
| Washington, D.C., : Mathematical Association of America, 1966 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
First concepts of topology : the geometry of mappings of segments, curves, circles and disks / / by William G. Chinn and N.E. Steenrod
| First concepts of topology : the geometry of mappings of segments, curves, circles and disks / / by William G. Chinn and N.E. Steenrod |
| Autore | Chinn William G |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Washington, D.C., : Mathematical Association of America, 1966 |
| Descrizione fisica | 1 online resource (viii, 160 pages) : digital, PDF file(s) |
| Disciplina | 513/.83 |
| Altri autori (Persone) | SteenrodNorman Earl <1910-1971.> |
| Collana | The Anneli Lax new mathematical library |
| Soggetto topico |
Topology
Geometry |
| ISBN | 0-88385-933-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- pt. I. Existence theorems in dimension 1. The first existence theorem ; Sets and functions ; Neighborhoods and continuity ; Open sets and closed sets ; The completeness of the real number system ; Compactness ; Connectedness ; Topological properties and topological equivalences ; A fixed point theorem ; Mappings of a circle into a line ; The pancake problems ; Zeros of polynomials -- pt. II. Existence theorems in dimension 2. Mappings of a plane into itself ; The disk ; Initial attempts to formulate the main theorem ; Curves and closed curves ; Intuitive definition of winding number ; Statement of the main theorem ; When is an argument not a-proof? ; The angle swept out by a curve ; Partitioning a curve into short curves ; The winding number W ; Properties of A and W ; Homotopies of curves ; Constancy of the winding number ; Proof of the main theorem ; The circle winds once about each interior point ; The fixed point property ; Vector fields ; The equivalence of vector fields and mappings ; The index of a vector field around a closed curve ; The mappings of a sphere into a plane ; Dividing a ham sandwich ; Vector fields tangent to a sphere ; Complex numbers ; Every polynomial has a zero ; Epilogue: A brief glance at higher dimensional cases -- Solutions for exercises. |
| Record Nr. | UNINA-9910964239103321 |
|
Chinn William G
|
||
| Washington, D.C., : Mathematical Association of America, 1966 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||