Topology :
Shick, Paul Louis, 1956-
Topology : point-set and geometric / Paul L. Shick. - 1 online resource (xiii, 271 pages) : illustrations. - Pure and applied mathematics . - Pure and applied mathematics (John Wiley & Sons : Unnumbered) .
Includes bibliographical references (pages 263-264) and index.
Front Matter -- Introduction: Intuitive Topology -- Background on Sets and Functions -- Topological Spaces -- More on Open and Closed Sets and Continuous Functions -- New Spaces from Old -- Connected Spaces -- Compact Spaces -- Separation Axioms -- Metric Spaces -- The Classification of Surfaces -- Fundamental Groups and Covering Spaces -- References -- Index -- Pure and Applied Mathematics. foreword -- Acknowledgments -- Introduction : Intuitive topology -- Introduction : intuitive topology -- Background on sets and functions -- Sets -- Functions -- Equivalence relations -- Induction -- Cardinal numbers -- Groups -- Topological spaces -- Introduction -- Definitions and examples -- Basics on open and closed sets -- The subspace topology -- Continuous functions -- More on open and closed sets and continuous functions -- Introduction -- Basis for a topology -- Limit points -- Interior, boundary and closure -- More on continuity -- New spaces from old -- Introduction -- Product spaces -- Infinite product spaces (optional) -- Quotient spaces -- Unions and wedges -- Connected spaces -- Introduction -- Definition, examples and properties -- Connectedness in the real line -- Path-connectedness -- Connectedness of unions and finite products -- Connnectedness of infinite products (optional) -- Compact spaces -- Introduction -- Definition, examples and properties -- Hausdorff spaces and compactness -- Compactness in the real line -- Compactness of products -- Finite intersection property (optional). 1. 1.1. 2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 3. 3.1. 3.2. 3.3. 3.4. 3.5. 4. 4.1. 4.2. 4.3. 4.4. 4.5. 5. 5.1. 5.2. 5.3. 5.4. 5.5. 6. 6.1. 6.2. 6.3. 6.4. 6.5. 6.6. 7. 7.1. 7.2. 7.3. 7.4. 7.5. 7.6. Separation axioms -- Introduction -- Definition and examples -- Regular and normal spaces -- Separation axioms and compactness -- Metric spaces -- Introduction -- Definition and examples -- Properties of metric spaces -- Basics on sequences -- The classification of surfaces -- Introduction -- Surfaces and higher-dimensional manifolds -- Connected sums of surfaces -- The classification theorem -- Triangulations of surfaces -- Proof of the classification theorem -- Euler characteristics and uniqueness -- Fundamental groups and covering spaces -- Introduction -- Homotopy of functions and paths -- An operation on paths -- The fundamental group -- Covering spaces -- Fundamental group of the circle and related spaces -- The fundamental groups of surfaces -- References -- Index. 8. 8.1. 8.2. 8.3. 8.4. 9. 9.1. 9.2. 9.3. 9.4. 10. 10.1. 10.2. 10.3. 10.4. 10.5. 10.6. 10.7. 11. 11. 1. 11.2. 11.3. 11.4. 11.5. 11.6. 11.7.
Use copy
This text covers the essentials of point-set topology in a relatively terse presentation, with lots of examples and motivation along the way. Along with the standard point-set topology topics (connected spaces, compact spaces, separation axioms, and metric spaces), the author includes path-connectedness, and a chapter on constructing spaces from other spaces (including products, quotients, etc.). The text culminates in to two main chapters, each independent of the other: 1) The Classification Theorem for Compact, Connected Surfaces and 2) Fundamental Groups and Covering Spaces, with Applications giving the reader the choice of which subject best suits them.
Electronic reproduction.
[S.l.] :
HathiTrust Digital Library,
2011.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
9781118031582 111803158X 9781118030585 1118030583
10.1002/9781118031582 Wiley InterScience http://www3.interscience.wiley.com
Algebraic topology.
Point set theory.
Topologie algébrique.
Ensembles de points (Mathématiques)
MATHEMATICS--Topology.
Algebraic topology.
Point set theory.
Topologie.
Ruimten (wiskunde)
Topologie.
Algebraische Topologie.
Electronic books.
Einführung.
QA612 / .S55 2007
514/.2
Topology : point-set and geometric / Paul L. Shick. - 1 online resource (xiii, 271 pages) : illustrations. - Pure and applied mathematics . - Pure and applied mathematics (John Wiley & Sons : Unnumbered) .
Includes bibliographical references (pages 263-264) and index.
Front Matter -- Introduction: Intuitive Topology -- Background on Sets and Functions -- Topological Spaces -- More on Open and Closed Sets and Continuous Functions -- New Spaces from Old -- Connected Spaces -- Compact Spaces -- Separation Axioms -- Metric Spaces -- The Classification of Surfaces -- Fundamental Groups and Covering Spaces -- References -- Index -- Pure and Applied Mathematics. foreword -- Acknowledgments -- Introduction : Intuitive topology -- Introduction : intuitive topology -- Background on sets and functions -- Sets -- Functions -- Equivalence relations -- Induction -- Cardinal numbers -- Groups -- Topological spaces -- Introduction -- Definitions and examples -- Basics on open and closed sets -- The subspace topology -- Continuous functions -- More on open and closed sets and continuous functions -- Introduction -- Basis for a topology -- Limit points -- Interior, boundary and closure -- More on continuity -- New spaces from old -- Introduction -- Product spaces -- Infinite product spaces (optional) -- Quotient spaces -- Unions and wedges -- Connected spaces -- Introduction -- Definition, examples and properties -- Connectedness in the real line -- Path-connectedness -- Connectedness of unions and finite products -- Connnectedness of infinite products (optional) -- Compact spaces -- Introduction -- Definition, examples and properties -- Hausdorff spaces and compactness -- Compactness in the real line -- Compactness of products -- Finite intersection property (optional). 1. 1.1. 2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 3. 3.1. 3.2. 3.3. 3.4. 3.5. 4. 4.1. 4.2. 4.3. 4.4. 4.5. 5. 5.1. 5.2. 5.3. 5.4. 5.5. 6. 6.1. 6.2. 6.3. 6.4. 6.5. 6.6. 7. 7.1. 7.2. 7.3. 7.4. 7.5. 7.6. Separation axioms -- Introduction -- Definition and examples -- Regular and normal spaces -- Separation axioms and compactness -- Metric spaces -- Introduction -- Definition and examples -- Properties of metric spaces -- Basics on sequences -- The classification of surfaces -- Introduction -- Surfaces and higher-dimensional manifolds -- Connected sums of surfaces -- The classification theorem -- Triangulations of surfaces -- Proof of the classification theorem -- Euler characteristics and uniqueness -- Fundamental groups and covering spaces -- Introduction -- Homotopy of functions and paths -- An operation on paths -- The fundamental group -- Covering spaces -- Fundamental group of the circle and related spaces -- The fundamental groups of surfaces -- References -- Index. 8. 8.1. 8.2. 8.3. 8.4. 9. 9.1. 9.2. 9.3. 9.4. 10. 10.1. 10.2. 10.3. 10.4. 10.5. 10.6. 10.7. 11. 11. 1. 11.2. 11.3. 11.4. 11.5. 11.6. 11.7.
Use copy
This text covers the essentials of point-set topology in a relatively terse presentation, with lots of examples and motivation along the way. Along with the standard point-set topology topics (connected spaces, compact spaces, separation axioms, and metric spaces), the author includes path-connectedness, and a chapter on constructing spaces from other spaces (including products, quotients, etc.). The text culminates in to two main chapters, each independent of the other: 1) The Classification Theorem for Compact, Connected Surfaces and 2) Fundamental Groups and Covering Spaces, with Applications giving the reader the choice of which subject best suits them.
Electronic reproduction.
[S.l.] :
HathiTrust Digital Library,
2011.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
9781118031582 111803158X 9781118030585 1118030583
10.1002/9781118031582 Wiley InterScience http://www3.interscience.wiley.com
Algebraic topology.
Point set theory.
Topologie algébrique.
Ensembles de points (Mathématiques)
MATHEMATICS--Topology.
Algebraic topology.
Point set theory.
Topologie.
Ruimten (wiskunde)
Topologie.
Algebraische Topologie.
Electronic books.
Einführung.
QA612 / .S55 2007
514/.2