Theories of dimension from ancient to modern times / Dale Martin Johnson.

Format:

Book

Author/Creator:

Johnson, Dale Martin, author.

Series:

Sources and studies in the history of mathematics and physical sciences

Sources and studies in the history of mathematics and physical sciences 2196-8810

Language:

English

Subjects (All):

Dimension theory (Topology).

Measure theory.

Physical Description:

xxi, 562 pages : illustrations, portraits, facsimiles ; 24 cm

Place of Publication:

Cham : Springer, [2025]

Summary:

This book provides a history and analysis of the ideas, problems, concepts, and theories of dimension from ancient to modern times.It focuses primarily on topological and, to a lesser extent, measure-theoretic approaches.

Contents:

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 Bolzanos 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, 18781879

8 Early Development of Point-Set Theory and Point-Set Topology

9 Poincars Theories of Dimension

10 Riesz, Baire, Frchet: New Approaches to Dimension

11 Brouwer: Development of Topology, Invariance of Dimension

12 New Ways of Proving Invariance of Dimension; BrouwerLebesgue Dispute

13 Problems of Curves and Dimension in the Early Twentieth Century

14 Urysohns Theory of Curves and Dimension

15 Mengers 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.

Notes:

Includes bibliographical references (pages 441-507) and index.

ISBN:

9783032026811

3032026814

OCLC:

1559901387

Publisher Number:

CIPO000319027