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First concepts of topology : the geometry of mappings of segments, curves, circles and disks / by William G. Chinn and N.E. Steenrod.
- Format:
- Book
- Author/Creator:
- Chinn, William G.
- Series:
- Anneli Lax New Mathematical Library
- The Anneli Lax new mathematical library ; 18
- Language:
- English
- Subjects (All):
- Topology.
- Geometry.
- Physical Description:
- 1 online resource (viii, 160 pages) : digital, PDF file(s).
- Edition:
- 1st ed.
- Place of Publication:
- Washington, D.C. : Mathematical Association of America, 1966.
- Language Note:
- English
- Summary:
- Over 150 problems and solutions.
- Contents:
- 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.
- Notes:
- Includes index.
- Description based on print version record.
- ISBN:
- 0-88385-933-5
- OCLC:
- 929120340
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