03114nam 2200589Ia 450 991096423910332120200520144314.00-88385-933-5(CKB)2670000000205150(EBL)3330421(SSID)ssj0000577613(PQKBManifestationID)11399460(PQKBTitleCode)TC0000577613(PQKBWorkID)10577925(PQKB)11192045(UkCbUP)CR9780883859339(Au-PeEL)EBL3330421(CaPaEBR)ebr10729392(OCoLC)929120340(RPAM)2642256(MiAaPQ)EBC3330421(EXLCZ)99267000000020515020111102d1966 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierFirst concepts of topology the geometry of mappings of segments, curves, circles and disks /by William G. Chinn and N.E. Steenrod1st ed.Washington, D.C. Mathematical Association of America19661 online resource (viii, 160 pages) digital, PDF file(s)The Anneli Lax new mathematical library ;18Includes index.0-88385-618-2 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.Over 150 problems and solutions.Anneli Lax New Mathematical LibraryTopologyGeometryTopology.Geometry.513/.83Chinn William G1196058Steenrod Norman Earl1910-1971.41684MiAaPQMiAaPQMiAaPQBOOK9910964239103321First concepts of topology4403600UNINA