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eBook A Geometric Introduction to Topology (Dover Books on Mathematics) epub

by C. T. C. Wall

eBook A Geometric Introduction to Topology (Dover Books on Mathematics) epub
  • ISBN: 0486678504
  • Author: C. T. C. Wall
  • Genre: Science
  • Subcategory: Mathematics
  • Language: English
  • Publisher: Dover Publications; Revised edition (January 17, 2011)
  • Pages: 192 pages
  • ePUB size: 1791 kb
  • FB2 size 1804 kb
  • Formats mobi docx doc lit


This book is a brief introduction to algebraic topology and is written by one of the major contributors to the subject. Written for undergraduates, it does not presuppose any background in topology, and the author concentrates strictly on subsets of Euclidean space.

This book is a brief introduction to algebraic topology and is written by one of the major contributors to the subject. And, interestingly, the author does not introduce homology and cohomology using simplicial complexes, but instead uses the Cech theory and singular homology.

A Geometric Introduction to Topology (Dover Books on Mathematics). These geometric objects in turn motivate a further discussion of set-theoretic topology and of its applications in function spaces. An introduction to homotopy and the fundamental group then brings the student's new theoretical knowledge to bear on very concrete problems: the calculation of the fundamental group of the circle and a proof of the fundamental theorem of algebra.

A geometric introduction to topology Wall C. T. C. Dover 9780486678504 Геометрическое . Dover 9780486678504 Геометрическое введение в топологию : Intended to provide a first course in algebraic topology to advanced undergraduates . Поставляется из: США Описание: Intended to provide a first course in algebraic topology to advanced undergraduates, this book introduces homotopy theory, the duality theorem and the relation of topological ideas to other branches of pure mathematics. It is unique in not presupposing a course in general topology and in avoiding the use of simplexes.

Title: A Geometric Introduction to Topology. Publisher: Dover Publications. Welcome to Our AbeBooks Store for books. Publication Date: 2011. I always strive to achieve best customer satisfaction and have always described book accurately. I got lot of Out of Print and Rare books in my store and still adding lot of books. I will ship book within 24 hours of confirmed payment. Visit Seller's Storefront. Terms of Sale: 100 % Customer Satisfaction is our Goal.

Nathan Altshiller-Court. Thank you Dover!! This is one of the two English books in print that give a fairly complete introduction to advanced Euclidean geometry, the other one being the comparable text by R A Johnson, Advanced Euclidean Geometry (Dover Books on Mathematics). The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev's book Kiselev's Geometry, Book I. Planimetry.

A Geometric Introduction to Topology book. Published January 17th 2011 by Dover Publications (first published December 1972). A Geometric Introduction to Topology. 0486678504 (ISBN13: 9780486678504).

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Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.

Intended to provide a first course in algebraic topology to advanced undergraduates, this book introduces homotopy theory, the duality theorem and the relation of topological ideas to other branches of pure mathematics. It is unique in not presupposing a course in general topology and in avoiding the use of simplexes. Exercises and problems at the end of each chapter. Indexes of terms and notations. 1972 edition.
Comments: (2)
Dyni
This book is a brief introduction to algebraic topology and is written by one of the major contributors to the subject. Written for undergraduates, it does not presuppose any background in topology, and the author concentrates strictly on subsets of Euclidean space. And, interestingly, the author does not introduce homology and cohomology using simplicial complexes, but instead uses the Cech theory and singular homology. Also, and somewhat disappointingly, the fundamental group is not discussed at all. The author is very concrete in his presentation, and he includes effective sets of exercises at the end of each chapter. He also introduces the necessary algebra at various places in the book.
Some of the highlights in the book include: 1. The discussion of the zeroth cohomology group of a topological space, which is introduced as the collection of continuous maps from the space into the integers. This of course is what is called singular cohomology, and the author shows how it is related to the path components of the space, one consequence being that if there is only one path component, then the zeroth cohomology group has only constant maps. The singular homology group is then defined as the free group on the path component space. 2. The treatment of homotopy, and how it is related to the first singular cohomology group, the latter being the collection of maps from a space to the unit circle. The author also gives an interesting exercise dealing with quaternions. 3. The study of the algebraic topology of the unit circle. This discussion introduces the important concept of the degree of a map, and this is used to prove the fundamental theorem of algebra and the Brouwer fixed point theorem in the plane. 4. The treatment of the Mayer-Vietoris theorem. This is a fundamental result in algebraic topology, and the author computes the first singular cohomology group of a product as an example of this result. 5. The discussion on duality, which, at this level, is a very original presentation that essentially relies on extending Eilenberg's criterion on separation of points by compact plane sets.
grand star
This book is based on an intersting idea -- a direct path to the duality theorem. But it has so many flaws. Definitions are often loose, there are no significant examples, proofs are often unclear. Some proofs used symbols never explicitly defined.
There is also a complete lack of motivation.
The worst Dover math book I have seen.
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