Theories of Dimension from Ancient to Modern Times

1 Introduction to Theories of Dimension.- 2 Ideas Touching on Dimension in Ancient Greek Philosophy and Mathematics.- 3 Dimension from the Middle Ages to the End of the Eighteenth Century.- 4 Bolzano’s Investigations into Geometry and Dimension.- 5 Nineteenth-Century Theories of Higher-Dimensional Spaces.- 6 Cantor and Dedekind: Discovery of a Counterintuitive Example concerning Dimension.- 7 Early Efforts to Prove Invariance of Dimension, 1878–1879.- 8 Early Development of Point-Set Theory and Point-Set Topology.- 9 Poincaré’s Theories of Dimension.- 10 Riesz, Baire, Fréchet: New Approaches to Dimension.- 11 Brouwer: Development of Topology, Invariance of Dimension.- 12 New Ways of Proving Invariance of Dimension; Brouwer–Lebesgue Dispute.- 13 Problems of Curves and Dimension in the Early Twentieth Century.- 14 Urysohn’s Theory of Curves and Dimension.- 15 Menger’s Theory of Curves and Dimension.- 16 Development of Theories of Dimension and Curves.- 17 Historical, Mathematical, and Philosophical Perspectives.- Appendix A: Original Language Texts of Quotations.

• Erscheinungsdatum: 31.10.2025
• Autor/Autorin: Dale Martin Johnson
• Reihe: History (R0)
• Format: E-Book
• Dateiformat: PDF
• Kopierschutz: Wasserzeichen
• Dateigröße: 34.1 MB
• Verlag: SPRINGER
• Sprache: Englisch
• Umfang: 562 Seiten
• ISBN: 9783032026828
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