Algebraical and Topological Foundations of Geometry
Proceedings of a Colloquium Held in Utrecht, August 1959
Published on 9. May 2014
216 pages
978-1-4831-8464-7 (ISBN)
Description
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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International Mathematical Union | H. Freudentha
Algebraical & Topological Foundations of Geometry
Proceedings of the College Utrecht, August 1959
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01/1962
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Content
¿Hjelmslevsche GeometrieZur Geometrischen Algebra der MöbiusebeneThe Theory of Parallels with Applications to Closed GeodesicsTactical Decompositions of ¿-SpacesSchwach Projektive Räume über Dreifachen TernärkörpernBericht über die Theorie der Rosenfeldschen Elliptischen EbenenSymplektische und Metasymplektische GeometrienOn Groups of HomeomorphismsTopological Descriptive PlanesComplemented Modular LatticesÜber die Topologische und Algebraische Struktur Topologischer Doppelloops und Einiger Topologischer Projektiver EbenenSome Results of Collineation GroupsExceptional Algebras and Exceptional GroupsAnordnungsfragen in Ternären Ringen und Allgemeinen Projektiven und Affinen EbenenConstruction Geometries and Construction FieldsProjektive Geometrie und Lineare Algebra über Verallgemeinerten BewertungsringenVerallgemeinerte Metrische Ebenen und Orthogonale GruppenAnneaux Ternaires et Corps Géneralisés Liés aux Géometries ¿¿¿-ArguésiennesDifferential Geometry and Analytic Group Theory Methods in Foundations of GeometryEinfache Lie-Gruppen und Nichteuklidische GeometrienTopologische Projektive EbenenVon Staudt Projectivities of Moufang PlanesVerallgemeinerte Affine Räume und ihre Algebraische DarstellungThe Projective Octave PlaneGroupes Algébriques Semi-Simples et Géometries AssociéesAn Axiomatic Treatment of Polar GeometryPerspectivities and the Little Projective Groups
