Algebraical and Topological Foundations of Geometry
eBook - PDF

Algebraical and Topological Foundations of Geometry

Proceedings of a Colloquium Held in Utrecht, August 1959

  1. 216 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Algebraical and Topological Foundations of Geometry

Proceedings of a Colloquium Held in Utrecht, August 1959

About this book

Algebraical and Topological Foundations of Geometry contains the proceedings of the Colloquium on Algebraic and Topological Foundations of Geometry, held in Utrecht, the Netherlands in August 1959. The papers review the algebraical and topological foundations of geometry and cover topics ranging from the geometric algebra of the Möbius plane to the theory of parallels with applications to closed geodesies. Groups of homeomorphisms and topological descriptive planes are also discussed. Comprised of 26 chapters, this book introduces the reader to the theory of parallels with applications to closed geodesies; groups of homeomorphisms; complemented modular lattices; and topological descriptive planes. Subsequent chapters focus on collineation groups; exceptional algebras and exceptional groups; the connection between algebra and constructions with ruler and compasses; and the use of differential geometry and analytic group theory methods in foundations of geometry. Von Staudt projectivities of Moufang planes are also considered, and an axiomatic treatment of polar geometry is presented. This monograph will be of interest to students of mathematics.

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Information

Publisher
Pergamon
Year
2014
Print ISBN
9780080096100
eBook ISBN
9781483184647
Topic
Mathematics
Subtopic
Geometry
Index
Mathematics

Table of contents

  1. Front Cover
  2. Algebraical and Topological Foundations of Geometry
  3. Copyright Page
  4. Table of Contents
  5. PREFACE
  6. CHAPTER 1. HJELMSLEVSCHE GEOMETRIE
  7. CHAPTER 2. ZUR GEOMETRISCHEN ALGEBRADER MÖBIUSEBENEN
  8. CHAPTER 3. THE THEORY OF PARALLELS WITH APPLICATIONS TO CLOSED GEODESICS
  9. CHAPTER 4. TACTICAL DECOMPOSITIONS OF λ-SPACES
  10. CHAPTER 5. SCHWACH PROJEKTIVE RÄUME ÜBER DREIFACHEN TERNÄRKÖRPERN
  11. CHAPTER 6. SYMPLEKTISCHE UND METASYMPLEKTISCHEGEOMETRIEN
  12. CHAPTER 7. BERICHT ÜBER DIE THEORIE DER ROSENFELDSCHEN ELLIPTISCHEN EBENEN
  13. CHAPTER 8. ON GROUPS OF HOMEOMORPHISMS
  14. CHAPTER 9. TOPOLOGICAL DESCRIPTIVE PLANES
  15. CHAPTER 10. COMPLEMENTED MODULAR LATTICES
  16. CHAPTER 11. ÜBER DIE TOPOLOGISCHE UND ALGEBRAISCHE STRUKTUR TOPOLOGISCHER DOPPELLOOPS UND EINIGER TOPOLOGISCHER PROJEKTIVER EBENEN
  17. CHAPTER 12. SOME RESULTS ON COLLINEATION GROUPS
  18. CHAPTER 13. ANORDNUNGSFRAGEN IN TERNÄREN RINGEN UND ALLGEMEINEN PROJEKTIVEN UND AFFINEN EBENEN
  19. CHAPTER 14. CONSTRUCTION GEOMETRIES AND CONSTRUCTION FIELDS
  20. CHAPTER 15. PROJEKTIVE GEOMETRIE UND LINEARE ALGEBRA ÜBER VERALLGEMEINERTEN BEWERTUNGSRINGEN
  21. CHAPTER 16. VERALLGEMEINERTE METRISCHE EBENEN UND ORTHOGONALE GRUPPEN
  22. CHAPTER 17. ANNEAUX TERNAIRES ET CORPS GÉNÉRALISES LIES AUX GÉOMÉTRIES NON-ARGUÉSIENNESt
  23. CHAPTER 18. DIFFERENTIAL GEOMETRY AND ANALYTIC GROUP THEORY METHODS IN FOUNDATIONS OF GEOMETRY
  24. CHAPTER 19. EINFACHE LIE-GRUPPEN UND NICHTEUKLIDISCHE GEOMETRIEN
  25. CHAPTER 20. TOPOLOGISCHE PROJEKTIVE EBENEN
  26. CHAPTER 21. VON STAUDT PROJECTIVITIESOF MOUFANG PLANES
  27. CHAPTER 22. VERALLGEMEINERTE AFPINE RÄUME UNDIHRE ALGEBRAISCHE DARSTELLUNG
  28. CHAPTER 23. THE PROJECTIVE OCTAVE PLANE
  29. CHAPTER 24. GROUPES ALGÉBRIQUES SEMI-SIMPLES ET GEOMETRIES ASSOCIÉES
  30. CHAPTER 25. AN AXIOMATIC TREATMENT OF POLARGEOMETRY
  31. CHAPTER 26. PERSPECTIVITIES AND THE LITTLEPROJECTIVE GROUP