First concepts of topology : the geometry of mappings of segments, curves, circles and disks / / by William G. Chinn and N.E. Steenrod
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| Autore: |
Chinn William G
|
| Titolo: |
First concepts of topology : the geometry of mappings of segments, curves, circles and disks / / by William G. Chinn and N.E. Steenrod
|
| Pubblicazione: | Washington, D.C., : Mathematical Association of America, 1966 |
| Edizione: | 1st ed. |
| Descrizione fisica: | 1 online resource (viii, 160 pages) : digital, PDF file(s) |
| Disciplina: | 513/.83 |
| Soggetto topico: | Topology |
| Geometry | |
| Altri autori: |
SteenrodNorman Earl <1910-1971.>
|
| Note generali: | Includes index. |
| 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. |
| 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.: | 9910964239103321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Anneli Lax New Mathematical Library