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Selecta Mathematica I

  • Book
  • © 2002

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Authors:
  1. Karl Menger
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Editors:
  1. Bert Schweizer

    1. Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Center, Amherst, USA

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  2. Abe Sklar

    1. Department of Mathematics, Illinois Institute of Technology, Chicago, USA

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  3. Karl Sigmund

    1. Institute of Mathematics, University of Vienna, Austria

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  4. Peter Gruber

    1. Institute of Analysis and Technical Mathematics, Technical University, Vienna, Austria

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  5. Edmund Hlawka

    1. Institute of Analysis and Technical Mathematics, Technical University, Vienna, Austria

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  6. Ludwig Reich

    1. Institute of Mathematics, University of Graz, Austria

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  7. Leopold Schmetterer

    1. Institute of Mathematics, University of Vienna, Austria

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Table of contents (43 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    1. Introduction

      • Bert Schweizer
      Pages 1-5

  3. Karl Menger and Vienna’s Golden Autumn

    1. Karl Menger and Vienna’s Golden Autumn

      • Karl Sigmund
      Pages 7-21

  4. Commentary on Menger’s Work on Dimension Theory

    1. Commentary on Menger’s Work on Dimension Theory

      • Dale M. Johnson
      Pages 23-32

  5. Selected Papers on Dimension Theory

    1. Front Matter

      Pages 33-33
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    2. Zur Dimensions- und Kurventheorie

      • Karl Menger
      Pages 35-56

    3. Das Hauptproblem über die dimensionelle Struktur der Räume

      • Karl Menger, L. E. J. Brouwer
      Pages 57-63

    4. Dimension und Zusammenhangsstufe

      • W. Hurewicz, K. Menger
      Pages 65-80

    5. “Allgemeine Räume und Cartesische Räume”. (Erste Mitteilung)

      • K. Menger, L. E. J. Brouwer
      Pages 81-87

    6. “Allgemeine Räume und Cartesische Räume”. Zweite Mitteilung: „Ueber umfassendste n~dimensionale Mengen“

      • K. Menger, L. E. J. Brouwer
      Pages 89-92

    7. Über die Dimension von Punktmengen III

      • Karl Menger
      Pages 93-118

    8. Axiomatische Einführung des Dimensionsbegriffes

      • Karl Menger
      Pages 119-127

    9. Remarques sur la théorie axiomatique de la dimension

      • Par C. Kuratowski, K. Menger
      Pages 129-134

    10. Über die Hinweise auf Brouwer in Urysohns Mémoire

      • Karl Menger
      Pages 135-139

    11. Commentary on Menger’s Work on Curve Theory and Topology

      • Tony Crilly, Alan Moran
      Pages 141-152

  6. Selected Papers on Curve Theory and Topology

    1. Front Matter

      Pages 153-153
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    2. Einige Überdeckungssätze der Punktmengenlehre

      • Karl Menger
      Pages 155-178

    3. Grundzüge einer Theorie der Kurven

      • Karl Menger
      Pages 179-208

    4. Grundzüge einer Theorie der Kurven

      • Karl Menger, L. E. J. Brouwer
      Pages 209-213

    5. THÉORIE DES ENSEMBLES. — Une forme abstraite du théorème de Borel-Lebesgue généralisé

      • M. Karl Menger, M. Élie Cartan
      Pages 215-217
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Keywords

About this book

Karl Menger, one of the founders of dimension theory, is among the most original mathematicians and thinkers of the twentieth century. He was a member of the Vienna Circle and the founder of its mathematical equivalent, the Viennese Mathematical Colloquium. Both during his early years in Vienna and, after his emigration, in the United States, Karl Menger made significant contributions to a wide variety of mathematical fields, and greatly influenced many of his colleagues. These two volumes contain Menger's major mathematical papers, based on his own selection from his extensive writings. They deal with topics as diverse as topology, geometry, analysis and algebra, and also include material on economics, sociology, logic and philosophy. The Selecta Mathematica is a monument to the diversity and originality of Menger's ideas.


Editors and Affiliations

  • Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Center, Amherst, USA

    Bert Schweizer

  • Department of Mathematics, Illinois Institute of Technology, Chicago, USA

    Abe Sklar

  • Institute of Mathematics, University of Vienna, Austria

    Karl Sigmund, Leopold Schmetterer

  • Institute of Analysis and Technical Mathematics, Technical University, Vienna, Austria

    Peter Gruber, Edmund Hlawka

  • Institute of Mathematics, University of Graz, Austria

    Ludwig Reich

Bibliographic Information

  • Book Title: Selecta Mathematica I

  • Authors: Karl Menger

  • Editors: Bert Schweizer, Abe Sklar, Karl Sigmund, Peter Gruber, Edmund Hlawka, Ludwig Reich, Leopold Schmetterer

  • DOI: https://doi.org/10.1007/978-3-7091-6110-4

  • Publisher: Springer Vienna

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag GmbH Austria, part of Springer Nature 2002

  • Hardcover ISBN: 978-3-211-83734-4Published: 08 April 2002

  • Softcover ISBN: 978-3-7091-4862-4Published: 13 December 2016

  • eBook ISBN: 978-3-7091-6110-4Published: 12 March 2013

  • Edition Number: 1

  • Number of Pages: X, 611

  • Additional Information: Reprint 2016 of the 2002 Edition

  • Topics: History of Mathematical Sciences, Analysis, Geometry, Topology

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