First concepts of topology : the geometry of mappings of segments, curves, circles, and disks [L. W. Singer New mathematical library, 18]

[1st ed.], 1st printing ; viii, 160 p. illus. 23 cm. ; LCCN: 66-20367 ; LC: QA611; Dewey: 513/.83 ; OCLC: 494807 ; paper wrappers ; ex-lib, stamps, label, date due, pocket ; 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. ; Chinn taught both in junior high and senior high schools in San Francisco where students enjoyed his humorous and witty approaches to classroom teaching. He maintained a mathematics "laboratory" for the gifted and was three years assistant to the Curriculum Coordinator of the San Francisco Unified School District. In addition, he was contributing editor of Science World for two years, participated in writing projects for SMSG, and served on numerous committees concerned with mathematics. ; Norman Earl Steenrod received a PHD from Princeton in 1936, working under the famous topologist S. Lefschetz. Almost all his papers have been concerned with algebraic topology. ; VG.…