History of Topology

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I.M. James
Elsevier, Aug 24, 1999 - Mathematics - 1056 pages
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Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.
As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
 

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Contents

Chapter 1 The emergence of topological dimension theory
1
Chapter 2 The concept of manifold 18501950
25
Chapter 3 Development of the concept of homotopy
65
Chapter 4 Development of the concept of a complex
103
Chapter 5 Differential forms
111
Chapter 6 The topological work of Henri Poincaré
123
Chapter 7 Weyl and the topology of continuous groups
169
Some remarks on the interaction of general Topology With Other Areas of Mathematics
199
Origins to 1953
631
Chapter 24 Stable algebraic topology 19451966
665
Chapter 25 A history of duality in algebraic topology
725
Chapter 26 A short history of Hspaces
747
Chapter 27 A history of rational homotopy theory
757
Chapter 28 History of homological algebra
797
Chapter 29 Topologists at conferences
837
Chapter 30 Topologists in Hitlers Germany
849

Chapter 9 Absolute neighborhood retracts and shape theory
241
Chapter 10 Fixed point theory
271
Chapter 11 Geometric aspects in the development of knot theory
301
Chapter 12 Topology and physics a historical essay
359
Chapter 13 Singularities
417
Chapter 14 One hundred years of manifold topology
435
Chapter 15 3dimensional topology up to 1960
449
Chapter 16 A short history of triangulation and related matters
491
Chapter 17 Graph theory
503
Chapter 18 The early development of algebraic topology
531
Chapter 19 From combinatorial topology to algebraic topology
561
Chapter 20 p3S2 H Hopf WK Clifford F Klein
575
Chapter 21 A history of cohomology theory
579
Chapter 22 Fibre bundles fibre maps
605
Chapter 31 The Japanese school of topology
863
Chapter 32 Some topologists
883
Chapter 33 Johann Benedikt Listing
909
Chapter 34 Poul Heegaard
925
Chapter 35 Luitzen Egbertus Jan Brouwer
947
Chapter 36 Max Dehn
965
Chapter 37 Jakob Nielsen and his contributions to topology
979
Chapter 38 Heinz Hopf
991
Chapter 39 Hans Freudenthal
1009
Chapter 40 Herbert Seifert 19071996
1021
Appendix Some dates
1029
Index
1033
Copyright

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Page 13 - — if to divide a continuum it suffices to consider as cuts a certain number of elements all distinguishable from one another, we say that this continuum is of one dimension ; if, on the contrary, to divide a continuum it is necessary to consider as cuts a system of elements themselves forming one or several continua, we shall say that this continuum is of several dimensions. "If to divide a continuum C, cuts which form one or several continua of one dimension suffice, we shall say that C is a...

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James, University of Oxford, UK.

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