Algebraical and Topological Foundations of Geometry - 1st Edition - ISBN: 9780080096100, 9781483184647

Algebraical and Topological Foundations of Geometry

1st Edition

Proceedings of a Colloquium Held in Utrecht, August 1959

Authors: Hans Freudenthal
eBook ISBN: 9781483184647
Imprint: Pergamon
Published Date: 1st January 1962
Page Count: 216
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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.

Table of Contents

Hjelmslevsche Geometrie

Zur Geometrischen Algebra der Möbiusebene

The Theory of Parallels with Applications to Closed Geodesics

Tactical Decompositions of λ-Spaces

Schwach Projektive Räume über Dreifachen Ternärkörpern

Bericht über die Theorie der Rosenfeldschen Elliptischen Ebenen

Symplektische und Metasymplektische Geometrien

On Groups of Homeomorphisms

Topological Descriptive Planes

Complemented Modular Lattices

Über die Topologische und Algebraische Struktur Topologischer Doppelloops und Einiger Topologischer Projektiver Ebenen

Some Results of Collineation Groups

Exceptional Algebras and Exceptional Groups

Anordnungsfragen in Ternären Ringen und Allgemeinen Projektiven und Affinen Ebenen

Construction Geometries and Construction Fields

Projektive Geometrie und Lineare Algebra über Verallgemeinerten Bewertungsringen

Verallgemeinerte Metrische Ebenen und Orthogonale Gruppen

Anneaux Ternaires et Corps Géneralisés Liés aux Géometries Νοη-Arguésiennes

Differential Geometry and Analytic Group Theory Methods in Foundations of Geometry

Einfache Lie-Gruppen und Nichteuklidische Geometrien

Topologische Projektive Ebenen

Von Staudt Projectivities of Moufang Planes

Verallgemeinerte Affine Räume und ihre Algebraische Darstellung

The Projective Octave Plane

Groupes Algébriques Semi-Simples et Géometries Associées

An Axiomatic Treatment of Polar Geometry

Perspectivities and the Little Projective Groups


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© Pergamon 1962
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About the Author

Hans Freudenthal

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