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A Combinatorial Introduction to Topology (Dover Books on Mathematics) Paperback – March 14, 1994

ISBN-13: 978-0486679662 ISBN-10: 0486679667 Edition: Reprint

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 320 pages
  • Publisher: Dover Publications; Reprint edition (March 14, 1994)
  • Language: English
  • ISBN-10: 0486679667
  • ISBN-13: 978-0486679662
  • Product Dimensions: 8.4 x 5.4 x 0.7 inches
  • Shipping Weight: 11.2 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #579,347 in Books (See Top 100 in Books)

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24 of 24 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on August 15, 2002
Format: Paperback
Historically, combinatorial topology was a precursor to what is now the field of algebraic topology, and this book gives an elementary introduction to the subject, directed towards the beginning student of topology or geometry. Due to its importance in applications, the physicist reader who is intending eventually to specialize in elementary particle physics will gain much in the perusal of this book.
Combinatorial topology can be viewed first as an attempt to study the properties of polyhedra and how they fit together to form more complicated objects. Conversely, one can view it as a way of studying complicated objects by breaking them up into elementary polyhedral pieces. The author takes the former view in this book, and he restricts his attention to the study of objects that are built up from polygons, with the proviso that vertices are joined to vertices and (whole) edges are joined to (whole) edges.
He begins the book with a consideration of the Euler formula, and as one example considers the Euler number of the Platonic solids, resulting in a Diophantine equation. This equation only has five solutions, the Platonic solids. The author then motivates the concept of a homeomorphism (he calls them "topological equivalences") by considering topological transformations in the plane. Using the notion of topological equivalence he defines the notions of cell, path, and Jordan curve. Compactness and connectedness are then defined, along with the general notion of a topological space.
Elementary notions from differential topology are then considered in chapter 2, with the reader encountering for the first time the connections between analysis and topology, via the consideration of the phase portraits of differential equations.
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16 of 16 people found the following review helpful By A Customer on May 7, 1997
Format: Paperback
Way back in 1980 I took a course at Oberlin College from Professor Henle in which he used this book (his own) as the text. Up until then I had been wavering as to a major, whether it should be in the hard sciences or Math. Michael Henle, his course, and this textbook decided me. I majored in Math.

The book gives a very hands on, concrete approach to what is a very abstract realm. An example that comes immediately to mind is the proof of the classification of manifolds, which comes down to a sequence of clever cut and paste operations on a large sheet with labeled edges. This text also has a curious sense of humor subtly hidden through it. Just look in the index under 'Man in the moon'. I dare you!

The exercises, which consist mostly of writing proofs, where there is very little notation and all your ideas have to be written out long-hand, are incredibly valuable for developing a logical mind. At least they were for me, back in 1980.
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15 of 15 people found the following review helpful By A Customer on July 6, 1996
Format: Paperback
I think this is Dover Publications best title in topology.There is a fantastic and thorough introduction to many ofthe finer theorems (e.g.: Brouwer's Fixed Point Theorem, Sperner's Lemma, etc.). I was absolutely captivated with the ease with which Dr. Henle explained some remarkably difficult concepts. Much time is spent on some of the more unusual topics for a text at this level, including homology and even the qualitative behavior of differential equations! A serious book, for advanced undergraduates and graduates. Very enriching, and a definite plus as a reference tool.
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