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First Course in Topology Continuity and Dimension

ISBN-10: 0821838849
ISBN-13: 9780821838846
Edition: 2006
Authors: John McCleary
List price: $38.00
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Description: How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23  More...

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Book details

List price: $38.00
Copyright year: 2006
Publisher: American Mathematical Society
Publication date: 4/7/2006
Binding: Paperback
Pages: 210
Size: 5.50" wide x 8.25" long x 0.50" tall
Weight: 0.594
Language: English

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introducedby Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time. Thegoal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

A little set theory
Metric and topological spaces
Geometric notions
Building new spaces from old
Connectedness Compactness
Homotopy and the fundamental group
Computations and covering spaces
The Jordan Curve Theorem
Simplicial complexes Homology
Bibliography
Notation Index
Subject Index

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