LEADER 03569nam 2200613Ia 450 001 9910461904403321 005 20200520144314.0 010 $a0-88385-933-5 035 $a(CKB)2670000000205150 035 $a(EBL)3330421 035 $a(SSID)ssj0000577613 035 $a(PQKBManifestationID)11399460 035 $a(PQKBTitleCode)TC0000577613 035 $a(PQKBWorkID)10577925 035 $a(PQKB)11192045 035 $a(UkCbUP)CR9780883859339 035 $a(MiAaPQ)EBC3330421 035 $a(Au-PeEL)EBL3330421 035 $a(CaPaEBR)ebr10729392 035 $a(OCoLC)929120340 035 $a(EXLCZ)992670000000205150 100 $a20111102d1966 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFirst concepts of topology$b[electronic resource] $ethe geometry of mappings of segments, curves, circles and disks /$fby William G. Chinn and N.E. Steenrod 210 $aWashington, D.C. $cMathematical Association of America$d1966 215 $a1 online resource (169 p.) 225 0 $aThe Anneli Lax new mathematical library ;$v18 300 $aIncludes index. 311 $a0-88385-618-2 327 $a""Front Cover""; ""First Concepts of Topology: The Geometry of Mappings of Segments, Curves, Circles, and Disks""; ""Copyright Page""; ""Contents""; ""Introduction""; ""Part I: Existence Theorems in Dimension 1""; ""1. The first existence theorem""; ""2. Sets and functions""; ""3. Neighborhoods and continuity""; ""4. Open sets and closed sets""; ""5. The completeness of the real number system""; ""6. Compactness""; ""7. Connectedness""; ""8. Topological properties and topological equivalences""; ""9. A fixed point theorem""; ""10. Mappings of a circle into a line"" 327 $a""11. The pancake problems""""12. Zeros of polynomials""; ""Part II: Existence Theorems in Dimension 2""; ""13. Mappings of a plane into itself""; ""14. The disk""; ""15. Initial attempts to formulate the main theorem""; ""16. Curves and closed curves""; ""17. Intuitive definition of winding number""; ""18. Statement of the main theorem""; ""19. When is an argument not a proof?""; ""20. The angle swept out by a curve""; ""21. Partitioning a curve into short curves""; ""22. The winding number W(I??, I?³)""; ""23. Properties of A(I??, I?³) and W(I??, I?³)""; ""24. Homotopies of curves"" 327 $a""25. Constancy of the winding number""""26. Proof of the main theorem""; ""27. The circle winds once about each interior point""; ""28. The fixed point property""; ""29. Vector fields""; ""30. The equivalence of vector fields and mappings""; ""31. The index of a vector field around a closed curve""; ""32. The mappings of a sphere into a plane""; ""33. Dividing a ham sandwich""; ""34. Vector fields tangent to a sphere""; ""35. Complex numbers""; ""36. Every polynomial has a zero""; ""37. Epilogue: A brief glance at higher dimensional cases""; ""Solutions for Exercises""; ""Index"" 327 $a""Back Cover"" 330 $aOver 150 problems and solutions. 410 0$aAnneli Lax New Mathematical Library 606 $aTopology 606 $aGeometry 608 $aElectronic books. 615 0$aTopology. 615 0$aGeometry. 676 $a514 700 $aChinn$b William G$0862638 701 $aSteenrod$b Norman Earl$f1910-1971.$041684 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910461904403321 996 $aFirst concepts of topology$91925632 997 $aUNINA