Matches in Harvard for { <http://id.lib.harvard.edu/aleph/001081020/catalog> ?p ?o. }
Showing items 1 to 21 of
21
with 100 items per page.
- catalog abstract "Presents topology as a unifying force for larger areas of mathematics through its application in existence theorems.".
- catalog contributor b1228921.
- catalog contributor b1228922.
- catalog contributor b1228923.
- catalog created "[1966]".
- catalog date "1966".
- catalog date "[1966]".
- catalog dateCopyrighted "[1966]".
- catalog description "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.".
- catalog description "Presents topology as a unifying force for larger areas of mathematics through its application in existence theorems.".
- catalog extent "viii, 160 p. :".
- catalog isPartOf "New mathematical library ; 18".
- catalog issued "1966".
- catalog issued "[1966]".
- catalog language "eng".
- catalog publisher "[New York] Random House".
- catalog subject "QA611 .C42".
- catalog subject "Topology.".
- catalog tableOfContents "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.".
- catalog title "First concepts of topology: the geometry of mappings of segments, curves, circles, and disks, by W. G. Chinn and N. E. Steenrod.".
- catalog type "text".