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Projektive Ebenen by Günter Pickert

Projektive Ebenen

by Günter Pickert
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Book cover type: Paperback
  • ISBN13: 9783642661495
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 374
  • Original Price: EUR 51.39
  • Language: German
  • Edition: 2. Aufl. 1975.
  • Item Weight: 617 grams
  • BISAC Subject(s): Geometry / General

In den letzten 25 Jahren hat sich aus der Untersuchung der Grund- lagen der ebenen projektiven Geometrie ein neues mathematisches Sachgebiet, das der projektiven Ebenen, entwickelt. Wahrend man friiher fast ausschlieBlich das kategorische Axiomensystem der reellen oder der komplexen Geometrie untersuchte, wobei vereinzelte Modelle abweichender Geometrien (nichtdesarguessche, nichtarchimedische) nur zum Zweck von Unabhangigkeitsbeweisen aufgestellt wurden, sollen in dem neuen Gebiet gerade die vielfiiltigen Moglichkeiten projektiver Ebenen, unter denen die reelle und die komplexe Ebene nur besondere FaIle darstellen, behandelt und einer systematischen Untersuchung zuganglich gemacht werden. Man hat also eine ahnliche Erscheinung vor sich wie bei der Entstehung der heutigen Algebra, und so ist es denn nicht verwunderlich, daB viele Algebraiker an der Gestaltung des neuen Gebietes wesentlichen Antell haben, wobei man sich allerdings noch dariiber streiten mag, was Ursache und was Wirkung ist. Genau so wenig nun, wie man etwa die Korpertheorie der Algebra als Grund- lagenforschung iiber unser Zahlsystem wird bezeichnen wollen, darf man die Theorie der projektiven Ebenen jetzt noch zu den Grundlagen der projektiven Geometrie rechnen; ja, manche Geometer werden sie iiberhaupt nicht mehr in der Geometrie dulden wollen. In mancher Hinsicht mag es fiir eine Darstellung der Theorie der projektiven Ebenen noch zu friih sein. Dennoch scheint es mir fiir die weitere Forschungsarbeit unbedingt erforderlich, das bisher Gewonnene zusammenzufassen.

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