東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Linked to FindBook

Google Book

Amazon

博客來

Theories of dimension from ancient to modern times

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theories of dimension from ancient to modern times/ by Dale Martin Johnson.
Author:	Johnson, Dale Martin.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xxi, 562 p. :ill. (chiefly col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Dimension theory (Topology) -
Online resource:	https://doi.org/10.1007/978-3-032-02682-8
ISBN:	9783032026828

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

Theories of dimension from ancient to modern times[electronic resource] /by Dale Martin Johnson. - Cham :Springer Nature Switzerland :2025. - xxi, 562 p. :ill. (chiefly col.), digital ;24 cm. - Sources and studies in the history of mathematics and physical sciences,2196-8829. - Sources and studies in the history of mathematics and physical sciences..

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.

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. It offers a detailed account of the contributions of key mathematicians who shaped dimension theory, including Bernard Bolzano, Bernhard Riemann, Georg Cantor, Richard Dedekind, Henri Poincaré, L.E.J. Brouwer, Paul Urysohn, Karl Menger, Witold Hurewicz, Paul Alexandroff, and Felix Hausdorff. The book examines the twists and turns in the development of the subject, including its controversies, and explores the philosophical aspects of its history. As the first in-depth historical study of dimension theory, it serves as a reference for historians and philosophers of mathematics. It also provides general historical background for students and researchers with broader mathematical interests.

ISBN: 9783032026828

Standard No.: 10.1007/978-3-032-02682-8doiSubjects--Topical Terms:

555698
Dimension theory (Topology)

LC Class. No.: QA611.3

Dewey Class. No.: 514

Theories of dimension from ancient to modern times
LDR:03084nmm a2200337 a 4500 001 2421719
003 DE-He213
005 20251101120409.0
006 m d
007 cr nn 008maaau
008 260505s2025 sz s 0 eng d
020 $a 9783032026828 $q (electronic bk.)
020 $a 9783032026811 $q (paper)
024 7 $a 10.1007/978-3-032-02682-8 $2 doi
035 $a 978-3-032-02682-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA611.3
072 7 $a PBX $2 bicssc
072 7 $a MAT015000 $2 bisacsh
072 7 $a PBX $2 thema
082 0 4 $a 514 $2 23
090 $a QA611.3 $b .J66 2025
100 1 $a Johnson, Dale Martin. $3 3802972
245 1 0 $a Theories of dimension from ancient to modern times $h [electronic resource] / $c by Dale Martin Johnson.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xxi, 562 p. : $b ill. (chiefly col.), digital ; $c 24 cm.
490 1 $a Sources and studies in the history of mathematics and physical sciences, $x 2196-8829
505 0 $a 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.
520 $a 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. It offers a detailed account of the contributions of key mathematicians who shaped dimension theory, including Bernard Bolzano, Bernhard Riemann, Georg Cantor, Richard Dedekind, Henri Poincaré, L.E.J. Brouwer, Paul Urysohn, Karl Menger, Witold Hurewicz, Paul Alexandroff, and Felix Hausdorff. The book examines the twists and turns in the development of the subject, including its controversies, and explores the philosophical aspects of its history. As the first in-depth historical study of dimension theory, it serves as a reference for historians and philosophers of mathematics. It also provides general historical background for students and researchers with broader mathematical interests.
650 0 $a Dimension theory (Topology) $3 555698
650 1 4 $a History of Mathematical Sciences. $3 1530523
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Sources and studies in the history of mathematics and physical sciences. $3 740893
856 4 0 $u https://doi.org/10.1007/978-3-032-02682-8
950 $a History (SpringerNature-41172)