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First Concepts of Topology : the Geometry of Mappings of Segments, Curves, Circles, and Disks

Author: W G Chinn; N E Steenrod
Publisher: Cambridge : Cambridge University Press, 2012.
Series: Anneli Lax new mathematical library.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Chinn, William G.
First Concepts of Topology.
Washington : Mathematical Association of America, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: W G Chinn; N E Steenrod
ISBN: 9780883859339 0883859335
OCLC Number: 775428767
Notes: Title from publishers bibliographic system (viewed on 30 Jan 2012).
Description: 1 online resource.
Contents: ""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""
Series Title: Anneli Lax new mathematical library.
Responsibility: W.G. Chinn, N.E. Steenrod.

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