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A first course in topology : continuity and dimension

Author: John McCleary
Publisher: Providence, RI : American Mathematical Society, ©2006.
Series: Student mathematical library, v. 31.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"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  Read more...
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Genre/Form: Textbooks
Lehrbuch
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: John McCleary
ISBN: 0821838849 9780821838846
OCLC Number: 62742675
Description: xii, 211 pages : illustrations ; 22 cm.
Contents: Introduction --
ch. 1. A little set theory --
Equivalence relations --
The Schröder-Berrnstein theorem --
The problem of invariance of dimension --
ch. 2. Metric and topological spaces --
Continuity --
ch. 3. Geometric notions --
ch. 4. Building new spaces from old --
Subspaces --
Products --
Quotients --
ch. 5. Connectedness --
Path-connectedness --
ch. 6. Compactness --
ch. 7. Homotopy and the fundamental group --
ch. 8. Computations and covering spaces --
ch. 9. The Jordan curve theorem --
Gratings and arcs --
The index of a point not on a Jordan curve --
A proof of the Jordan curve theorem --
ch. 10. Simplicial complexes --
Simplicial mappings and barycentric subdivision --
ch. 11. Homology --
Homology and simplicial mappings --
Topological invariance --
Where from here? --
Bibliography --
Notation index --
Subject index.
Series Title: Student mathematical library, v. 31.
Responsibility: John McCleary.
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Abstract:

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  Read more...

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