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The Resource A first course in topology : continuity and dimension, John McCleary

A first course in topology : continuity and dimension, John McCleary

Creator
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 answer this question, some important topological ideas were introduced by 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. The goal 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."--Publisher's website
Language
eng
Work
Publication
Extent
xii, 211 pages
Contents
  • Continuity
  • ch. 3.
  • Geometric notions
  • ch. 4.
  • Building new spaces from old
  • Subspaces
  • Products
  • Quotients
  • ch. 5.
  • Connectedness
  • Introduction
  • 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
  • ch. 1.
  • 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?
  • A little set theory
  • Bibliography
  • Notation index
  • Subject index
  • Equivalence relations
  • The Schröder-Berrnstein theorem
  • The problem of invariance of dimension
  • ch. 2.
  • Metric and topological spaces
Isbn
9780821838846
Instance
Label
A first course in topology : continuity and dimension
Title
A first course in topology
Title remainder
continuity and dimension
Statement of responsibility
John McCleary
Creator
Subject
Genre
Language
eng
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 answer this question, some important topological ideas were introduced by 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. The goal 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."--Publisher's website
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1952-
http://library.link/vocab/creatorName
McCleary, John
Dewey number
514
Illustrations
illustrations
Index
index present
LC call number
QA611
LC item number
.M38 2006
Literary form
non fiction
Nature of contents
bibliography
Series statement
Student mathematical library,
Series volume
v. 31
http://library.link/vocab/subjectName
Topology
Label
A first course in topology : continuity and dimension, John McCleary
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 201-205) and indexes
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Continuity
  • ch. 3.
  • Geometric notions
  • ch. 4.
  • Building new spaces from old
  • Subspaces
  • Products
  • Quotients
  • ch. 5.
  • Connectedness
  • Introduction
  • 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
  • ch. 1.
  • 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?
  • A little set theory
  • Bibliography
  • Notation index
  • Subject index
  • Equivalence relations
  • The Schröder-Berrnstein theorem
  • The problem of invariance of dimension
  • ch. 2.
  • Metric and topological spaces
Control code
62742675
Dimensions
22 cm
Extent
xii, 211 pages
Isbn
9780821838846
Isbn Type
(alk. paper)
Lccn
2005058915
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
Label
A first course in topology : continuity and dimension, John McCleary
Publication
Bibliography note
Includes bibliographical references (pages 201-205) and indexes
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Continuity
  • ch. 3.
  • Geometric notions
  • ch. 4.
  • Building new spaces from old
  • Subspaces
  • Products
  • Quotients
  • ch. 5.
  • Connectedness
  • Introduction
  • 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
  • ch. 1.
  • 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?
  • A little set theory
  • Bibliography
  • Notation index
  • Subject index
  • Equivalence relations
  • The Schröder-Berrnstein theorem
  • The problem of invariance of dimension
  • ch. 2.
  • Metric and topological spaces
Control code
62742675
Dimensions
22 cm
Extent
xii, 211 pages
Isbn
9780821838846
Isbn Type
(alk. paper)
Lccn
2005058915
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations

Subject

Genre

Member of

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      38.944377 -92.326537

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