Topological Circle Planes and Topological Quandrangles (Research Notes in Mathematics, 337, Band 337).

Schroth, Andreas E.:

ISBN 10: 0582288118 / ISBN 13: 9780582288119

Editore: CRC Press, 1995

Riguardo questo articolo

166 S. Das Buch ist in exzellentem, sauberen Zustand. -----Inhalt:. This research note presents a complete treatment of the connection between topological circle planes and topological generalized quadrangles. The author uses this connection to provide a better understanding of the relationships between different types of circle planes and to solve a topological version of the problem of Apollonius. Topological Circle Planes and Topological Quadrangles begins with a foundation in classical circle planes and the real symmetric generalized quadrangle and the connection between them. This provides a solid base from which the author offers a more generalized exploration of the topological case. He also compares this treatment to the finite case. Subsequent chapters examine Laguerre, Möbius, and Minkowski planes and their respective relationships to antiregular quadrangles. The author addresses the Lie geometry of each and discuss the relationships of circle planes-the "sisters" of Möbius, Laguerre, and Minkowski planes - and concludes by solving a topological version of the problem of Apollonius in Laguerre, Möbius, and Minkowski planes. The treatment offered in this volume offers complete coverage of the topic. The first part of the text is accessible to anyone with a background in analytic geometry, while the second part requires basic knowledge in general and algebraic topology. Researchers interested in geometry-particularly in topological geometry-will find this volume intriguing and informative. Most of the results presented are new and can be applied to various problems in the field of topological circle planes. Introduction, Circle Planes, Introduction, Definitions and Notation, Models for Classical Circle Planes, Derived Structures, Antiregular Quadrangles, Introduction, Generalized Quadrangles, Square Projections, The Twisting Number, Antiregular Quadrangles, Characterization of Antiregular Quadrangles, Laguerre Planes and Antiregular Quadrangles, Introduction , Laguerre Planes Constructed from Antiregular Quadrangles, Antiregular Quadrangles Constructed from Laguerre Planes, Constructing Topologies on the Lie Geometry, Möbius Planes and Antiregular Quadrangles, Introduction , The Lie Geometry of a Möbius Plane, The Lifted Lie Geometry of a Flat Möbius Plane, Constructing Topologies on the Lifted Lie Geometry, Characterizing Quadrangles Obtained from Flat Möbius Planes, Minkowski Planes and Antiregular Quadrangles, Introduction, The Point Space and Parallel Classes, The Circle Space, The Other Spaces, The Derivation of a Minkowski Plane, The Lie Geometry of a Minkowski Plane, The Lifted Lie Geometry of a Minkowski Plane, The Topology on the Lifted Lie Geometry, Characterizing Quadrangles Obtained from Minkowski Planes, Relationship of Circle Planes, Introduction , Sisters of Laguerre Planes, Sisters of Möbius Planes, Sisters of Minkowski Planes, The Problem of Apollonius, Introduction, The Problem of Apollonius in Laguerre Planes, The Problem of Apollonius in Möbius Planes, One Point and Two Circles, Three Circles, The Problem of Apollonius in Minkowski Planes, Two Points and One Circle, One Point and Two circles, Three Circles, Index, Glossary, References ISBN: 9780582288119 Wir senden umgehend mit beiliegender MwSt.Rechnung. Sprache: Englisch Gewicht in Gramm: 295.

Codice articolo 669110

Dati bibliografici

• Titolo: Topological Circle Planes and Topological Quandrangles (Research Notes in Mathematics, 337, Band 337).
• Editore: CRC Press
• Data di pubblicazione: 1995
• Lingua: Inglese
• ISBN 10: 0582288118
• ISBN 13: 9780582288119
• Rilegatura: Broschur, Gr.-8°
• Condizione: Wie neu
• Peso: 295 grammi
• Cataloghi dei venditori:
  • Mathematik

Descrizione articolo

Riassunto

This research note presents a complete treatment of the connection between topological circle planes and topological generalized quadrangles. The author uses this connection to provide a better understanding of the relationships between different types of circle planes and to solve a topological version of the problem of Apollonius. Topological Circle Planes and Topological Quadrangles begins with a foundation in classical circle planes and the real symmetric generalized quadrangle and the connection between them. This provides a solid base from which the author offers a more generalized exploration of the topological case. He also compares this treatment to the finite case. Subsequent chapters examine Laguerre, Möbius, and Minkowski planes and their respective relationships to antiregular quadrangles. The author addresses the Lie geometry of each and discuss the relationships of circle planes-the "sisters" of Möbius, Laguerre, and Minkowski planes - and concludes by solving a topological version of the problem of Apollonius in Laguerre, Möbius, and Minkowski planes. The treatment offered in this volume offers complete coverage of the topic. The first part of the text is accessible to anyone with a background in analytic geometry, while the second part requires basic knowledge in general and algebraic topology. Researchers interested in geometry-particularly in topological geometry-will find this volume intriguing and informative. Most of the results presented are new and can be applied to various problems in the field of topological circle planes. Features

Informazioni sull?autore

Andreas E Schroth