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 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
- 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
- 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 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
- 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 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
- 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
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