Algebraical and Topological Foundations of Geometry
Proceedings of a Colloquium Held in Utrecht, August 1959
- 216 pages
- English
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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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Table of contents
- Front Cover
- Algebraical and Topological Foundations of Geometry
- Copyright Page
- Table of Contents
- PREFACE
- CHAPTER 1. HJELMSLEVSCHE GEOMETRIE
- CHAPTER 2. ZUR GEOMETRISCHEN ALGEBRADER MĂBIUSEBENEN
- CHAPTER 3. THE THEORY OF PARALLELS WITH APPLICATIONS TO CLOSED GEODESICS
- CHAPTER 4. TACTICAL DECOMPOSITIONS OF λ-SPACES
- CHAPTER 5. SCHWACH PROJEKTIVE RĂUME ĂBER DREIFACHEN TERNĂRKĂRPERN
- CHAPTER 6. SYMPLEKTISCHE UND METASYMPLEKTISCHEGEOMETRIEN
- CHAPTER 7. BERICHT ĂBER DIE THEORIE DER ROSENFELDSCHEN ELLIPTISCHEN EBENEN
- CHAPTER 8. ON GROUPS OF HOMEOMORPHISMS
- CHAPTER 9. TOPOLOGICAL DESCRIPTIVE PLANES
- CHAPTER 10. COMPLEMENTED MODULAR LATTICES
- CHAPTER 11. ĂBER DIE TOPOLOGISCHE UND ALGEBRAISCHE STRUKTUR TOPOLOGISCHER DOPPELLOOPS UND EINIGER TOPOLOGISCHER PROJEKTIVER EBENEN
- CHAPTER 12. SOME RESULTS ON COLLINEATION GROUPS
- CHAPTER 13. ANORDNUNGSFRAGEN IN TERNĂREN RINGEN UND ALLGEMEINEN PROJEKTIVEN UND AFFINEN EBENEN
- CHAPTER 14. CONSTRUCTION GEOMETRIES AND CONSTRUCTION FIELDS
- CHAPTER 15. PROJEKTIVE GEOMETRIE UND LINEARE ALGEBRA ĂBER VERALLGEMEINERTEN BEWERTUNGSRINGEN
- CHAPTER 16. VERALLGEMEINERTE METRISCHE EBENEN UND ORTHOGONALE GRUPPEN
- CHAPTER 17. ANNEAUX TERNAIRES ET CORPS GĂNĂRALISES LIES AUX GĂOMĂTRIES NON-ARGUĂSIENNESt
- CHAPTER 18. DIFFERENTIAL GEOMETRY AND ANALYTIC GROUP THEORY METHODS IN FOUNDATIONS OF GEOMETRY
- CHAPTER 19. EINFACHE LIE-GRUPPEN UND NICHTEUKLIDISCHE GEOMETRIEN
- CHAPTER 20. TOPOLOGISCHE PROJEKTIVE EBENEN
- CHAPTER 21. VON STAUDT PROJECTIVITIESOF MOUFANG PLANES
- CHAPTER 22. VERALLGEMEINERTE AFPINE RĂUME UNDIHRE ALGEBRAISCHE DARSTELLUNG
- CHAPTER 23. THE PROJECTIVE OCTAVE PLANE
- CHAPTER 24. GROUPES ALGĂBRIQUES SEMI-SIMPLES ET GEOMETRIES ASSOCIĂES
- CHAPTER 25. AN AXIOMATIC TREATMENT OF POLARGEOMETRY
- CHAPTER 26. PERSPECTIVITIES AND THE LITTLEPROJECTIVE GROUP