The Resource Basic topology, M.A. Armstrong

Basic topology, M.A. Armstrong

Label
Basic topology
Title
Basic topology
Statement of responsibility
M.A. Armstrong
Creator
Subject
Genre
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Armstrong, M. A.
Illustrations
illustrations
Index
index present
LC call number
QA611
LC item number
.A68 1983
Literary form
non fiction
Nature of contents
bibliography
Series statement
Undergraduate texts in mathematics.
http://library.link/vocab/subjectName
  • Topology
  • Topologie
  • Topology
  • Topologie
  • Topologie
  • Einführung
  • Topologie
Label
Basic topology, M.A. Armstrong
Instantiates
Publication
Note
Includes index
Bibliography note
Bibliography: p. 244-245
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
1. Introduction -- 1.1 Euler's theorem -- 1.2 Topological equivalence -- 1.3 Surfaces -- 1.4 Abstract spaces -- 1.5 A classification theorem -- 1.6 Topological invariants -- 2. Continuity -- 2.1 Open and closed sets -- 2.2 Continuous functions -- 2.3 A space-filling curve -- 2.4 The Tietze extension theorem -- 3. Compactness and connectedness -- 3.1 Closed bounded subsets of E[n] -- 3.2 The Heine-Borel theorem -- 3.3 Properties of compact spaces -- 3.4 Product spaces -- 3.5 Connectedness -- 3.6 Joining points by paths -- 4. Identification spaces -- 4.1 Constructing a Möbius strip -- 4.2 The identification topology -- 4.3 Topological groups -- 4.4 Orbit spaces -- 5. The fundamental group -- 5.1 Homotopic maps -- 5.2 Construction of the fundamental group -- 5.3 Calculations -- 5.4 Homotopy type -- 5.5 The Brouwer fixed-point theorem -- 5.6 Separation of the plane -- 5.7 The boundary of a surface -- 6. Triangulations -- 6.1 Triangulating spaces -- 6.2 Barycentric subdivision -- 6.3 Simplicial approximation -- 6.4 The edge group of a complex -- 6.5 Triangulating orbit spaces -- 6.6 Infinite complexes -- 7. Surfaces -- 7.1 Classification -- 7.2 Triangulation and orientation -- 7.3 Euler characteristics -- 7.4 Surgery -- 7.5 Surface symbols -- 8. Simplicial homology -- 8.1 Cycles and boundaries -- 8.2 Homology groups -- 8.3 Examples -- 8.4 Simplicial maps -- 8.5 Stellar subdivision -- 8.6 Invariance -- 9. Degree and Lefschetz number -- 9.1 Maps of spheres -- 9.2 The Euler-Poincaré formula -- 9.3 The Borsuk-Ulam theorem -- 9.4 The Lefschetz fixed-point theorem -- 9.5 Dimension -- 10. Knots and covering spaces -- 10.1 Examples of knots -- 10.2 The knot group -- 10.3 Seifert surfaces -- 10.4 Covering spaces -- 10.5 The Alexander polynomial -- Appendix: Generators and relations
Dimensions
25 cm.
Extent
xii, 251 pages
Isbn
9780387908397
Lccn
83000655
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)09392416
  • (OCoLC)ocm09392416
Label
Basic topology, M.A. Armstrong
Publication
Note
Includes index
Bibliography note
Bibliography: p. 244-245
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
1. Introduction -- 1.1 Euler's theorem -- 1.2 Topological equivalence -- 1.3 Surfaces -- 1.4 Abstract spaces -- 1.5 A classification theorem -- 1.6 Topological invariants -- 2. Continuity -- 2.1 Open and closed sets -- 2.2 Continuous functions -- 2.3 A space-filling curve -- 2.4 The Tietze extension theorem -- 3. Compactness and connectedness -- 3.1 Closed bounded subsets of E[n] -- 3.2 The Heine-Borel theorem -- 3.3 Properties of compact spaces -- 3.4 Product spaces -- 3.5 Connectedness -- 3.6 Joining points by paths -- 4. Identification spaces -- 4.1 Constructing a Möbius strip -- 4.2 The identification topology -- 4.3 Topological groups -- 4.4 Orbit spaces -- 5. The fundamental group -- 5.1 Homotopic maps -- 5.2 Construction of the fundamental group -- 5.3 Calculations -- 5.4 Homotopy type -- 5.5 The Brouwer fixed-point theorem -- 5.6 Separation of the plane -- 5.7 The boundary of a surface -- 6. Triangulations -- 6.1 Triangulating spaces -- 6.2 Barycentric subdivision -- 6.3 Simplicial approximation -- 6.4 The edge group of a complex -- 6.5 Triangulating orbit spaces -- 6.6 Infinite complexes -- 7. Surfaces -- 7.1 Classification -- 7.2 Triangulation and orientation -- 7.3 Euler characteristics -- 7.4 Surgery -- 7.5 Surface symbols -- 8. Simplicial homology -- 8.1 Cycles and boundaries -- 8.2 Homology groups -- 8.3 Examples -- 8.4 Simplicial maps -- 8.5 Stellar subdivision -- 8.6 Invariance -- 9. Degree and Lefschetz number -- 9.1 Maps of spheres -- 9.2 The Euler-Poincaré formula -- 9.3 The Borsuk-Ulam theorem -- 9.4 The Lefschetz fixed-point theorem -- 9.5 Dimension -- 10. Knots and covering spaces -- 10.1 Examples of knots -- 10.2 The knot group -- 10.3 Seifert surfaces -- 10.4 Covering spaces -- 10.5 The Alexander polynomial -- Appendix: Generators and relations
Dimensions
25 cm.
Extent
xii, 251 pages
Isbn
9780387908397
Lccn
83000655
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)09392416
  • (OCoLC)ocm09392416

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