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History of Topology
 
 

History of Topology [Hardcover]

I. M. James (Editor)
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

0444823751 978-0444823755 March 13, 2006 1
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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Editorial Reviews

Review

...This volume contains forty articles covering a wide range of topics including the interaction of topology with other branches of mathematics.... The articles reflect a variety of viewpoints and some deal with the lives of mathematicians who have contributed to the subject. Most mathematicians and many science historians wil find much of interest...
Aslib Book Guide, Vol. 64, No. 12
...it is not possible in the space of a review to do full justice to this magnificent volume, which combines scholarship, namely the bringing of past rends to current view in the light of later developments, with excellent exposition...
The London Mathematical Society Newsletter
....The book's editor, I.M. James, himself a distinguished topologist, has drawn together more than 40 authors for this account. ......the reader enjoys a consistently rich but varied diet....
Nature, Vol. 406
Daniel S. Silver
....despite its physical weight this collection of forty articles is not easy to put down. Anyone who spends time with this book will come away with a sense of the profound depth and epix scope of the youngest classical area of mathematics.......The reader who takes up History of Topology will find much more than space permits me to describe. That is as it should be, for topology is a rich terrain with boundaries that will continue to widen as we learn to see.
Alabama Journal of Mathematics
K. Sigmund
The editor, who himself has lived and shaped part of this history for the last fifty years, has done a superb job in choosing the right contributors and leaving them a considerable amount of liberty.
Monatshefte fur Mathematik

Product Details

  • Hardcover: 1068 pages
  • Publisher: North Holland; 1 edition (March 13, 2006)
  • Language: English
  • ISBN-10: 0444823751
  • ISBN-13: 978-0444823755
  • Product Dimensions: 9.5 x 6.8 x 2.1 inches
  • Shipping Weight: 4.8 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,543,438 in Books (See Top 100 in Books)

 

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5 of 5 people found the following review helpful:
5.0 out of 5 stars A lot of very good essays, March 2, 2005
By 
Colin McLarty (Chardon, OH USA) - See all my reviews
This review is from: History of Topology (Hardcover)
This book collects 40 essays on various themes, events, and personalities in the history of topology. I have browsed half of them and carefully read 6 or 8. Plus I have used the book as a reference, and so gained isolated facts from many of the essays.

The essays assume various amounts of background, proportionate to their subjects. In generally they are very clear and if you have any knowledge at all of a topic you can read an essay on it here at least well enough to decide if you want to work harder on it.

The book concentrates more on manifolds, fixed point theorems, algebraic topology, and homological algebra, than on issues in general or point set topology. It covers Poincare, Brouwer, Weyl, and gets up to derived categories. It could not possibly cover everything in that range. For one, Lefschetz is mentioned often but he could well have deserved a whole article on himself. Or there could have been an article on the Princeton school. But incomplete we must all resign ourselves to be.

The book is a huge amount of information, very well organized and presented.
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4 of 7 people found the following review helpful:
5.0 out of 5 stars Absolutely Brilliant, December 25, 2000
By A Customer
This review is from: History of Topology (Hardcover)
A sublime account of the history of topology from it's earliest incarnation as analysis situs to contemporary research.

No home should be without one.

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Inside This Book (learn more)
First Sentence:
The concept of dimension, deriving from our understanding of the dimensions of physical space, is one of the most interesting from a mathematical point of view. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
stable algebraic topology, cochain algebra models, commutative cochain algebra, homotopic change, topology colloquium, cochain algebras, modern knot theory, simplicial spectra, strong shape theory, topologisk teori, torsion gaps, rational homotopy theory, braid motions, stable homotopy category, fixed point class, cohomotopy groups, finite loop space, homotopy concept, homotopy theorists, metric compacta, translation invariant integral, order cohomology operations, shrinking criterion, loop space homology, local cut points
Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Mac Lane, Heinz Hopf, Jakob Nielsen, Mathematische Annalen, Comptes Rendus, Annals of Mathematics, London Math, Elsevier Science, Princeton Univ, Henri Poincaré, Poul Heegaard, United States, Academic Press, Acta Math, Henri Cartan, Max Dehn, University of Tokyo, Hans Freudenthal, Cambridge Univ, University of Copenhagen, Pures Appl, Emmy Noether, Hassler Whitney, Hermann Weyl
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