The Resource A first course in topology : continuity and dimension, John McCleary
A first course in topology : continuity and dimension, John McCleary
Resource Information
The item A first course in topology : continuity and dimension, John McCleary represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item A first course in topology : continuity and dimension, John McCleary represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 pointset 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 semesterlong 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
 Extent
 xii, 211 pages
 Contents

 Continuity
 ch. 3.
 Geometric notions
 ch. 4.
 Building new spaces from old
 Subspaces
 Products
 Quotients
 ch. 5.
 Connectedness
 Introduction
 Pathconnectedness
 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 SchröderBerrnstein theorem
 The problem of invariance of dimension
 ch. 2.
 Metric and topological spaces
 Isbn
 9780821838846
 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
 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 pointset 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 semesterlong 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
 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
 Bibliography note
 Includes bibliographical references (pages 201205) 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
 Pathconnectedness
 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 SchröderBerrnstein 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
 Bibliography note
 Includes bibliographical references (pages 201205) 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
 Pathconnectedness
 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 SchröderBerrnstein 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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