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First Concepts of Topology~tqw~_darksiderg

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INFO

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Title................: First Concepts of Topology 

Type.................: Ebook

Reader...............: PDF Reader

Size.................: 6.45 MB

Torrent Hash.........: D553CB0290ECC6110034BAAC2B281A7D03FF52D3

Posted by............: ~tqw~



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CONTENTS

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http://images.barnesandnoble.com/images/8770000/8770554.jpg

Synopsis:

Our purpose in writing this book is to show how topology arose, develop

a few of its elements, and present some of its simpler applications.

Topology came to be recognized as a distinct area of mathematics

about fifty years ago, and its major growth has taken place within the

last thirty years. It is the most vigorous of the newer branches of mathematics

and has been producing strong repercussions in most of the older

branches. It got its start in response to the needs of analysis (the part

of mathematics containing calculus and differential equations). However,

topology is not a branch of analysis. Instead, it is a kind of geometry. It

is not an advanced form of geometry such as projective or differential

geometry, but rather a primitive, rudimentary form-one which underlies

all geometries. A striking fact about topology is that its ideas have penetrated

nearly all areas of mathematics. In most of these applications,

topology supplies essential tools and concepts for proving certain basic

propositions known as existence theorems.



Table Of Contents:

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(<p, y)

23. Properties of A(<p, y) and W(<p, y)

24. Homotopies of curves 98

25. Constancy of the winding number 102

26. Proof of the main theorem 106

27. The circle winds once about each interior point 106

28. The fixed point property 108

29. Vector fields 110

30. The equivalence of vector fields and mappings 112

31. The index of a vector field around a closed curve 114

32. The mappings of a sphere into a plane 116

33. Dividing a ham sandwich 120

34. Vector fields tangent to a sphere 123

35. Complex numbers 127

36. Every polynomial has a zero 130

37. Epilogue: A brief glance at higher dimensional cases 133

Solutions for Exercises 137

Index 159



Product Details:

    * Pub. Date: June 1975

    * Publisher: Mathematical Association of America

    * Format: Textbook Paperback, 160pp

    * Sales Rank: 357,589

    * Series: New Mathematical Library Series

    * ISBN-13: 9780883856185

    * ISBN: 0883856182

    * Edition Number: 1



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Greetz Fellow UL'ers

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       mazuki `jedi Flatline newartriot aXXo KingBen Paulx1 unisonband

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