Topology [electronic resource] : point-set and geometric / Paul L. Shick.
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-connected...
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Full Text (via Wiley) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hoboken, N.J. :
Wiley-Interscience,
©2007.
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| Series: | Pure and applied mathematics (John Wiley & Sons : Unnumbered)
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| Subjects: |
MARC
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| 100 | 1 | |a Shick, Paul Louis, |d 1956- |0 http://id.loc.gov/authorities/names/n87109965 |1 http://isni.org/isni/0000000031042001. | |
| 245 | 1 | 0 | |a Topology |h [electronic resource] : |b point-set and geometric / |c Paul L. Shick. |
| 260 | |a Hoboken, N.J. : |b Wiley-Interscience, |c ©2007. | ||
| 300 | |a 1 online resource (xiii, 271 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
| 338 | |a online resource |b cr |2 rdacarrier. | ||
| 490 | 1 | |a Pure and applied mathematics. | |
| 505 | 0 | |a 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. | |
| 504 | |a Includes bibliographical references (pages 263-264) and index. | ||
| 505 | 0 | 0 | |t foreword -- |t Acknowledgments -- |g 1. |t Introduction : Intuitive topology -- |g 1.1. |t Introduction : intuitive topology -- |g 2. |t Background on sets and functions -- |g 2.1. |t Sets -- |g 2.2. |t Functions -- |g 2.3. |t Equivalence relations -- |g 2.4. |t Induction -- |g 2.5. |t Cardinal numbers -- |g 2.6. |t Groups -- |g 3. |t Topological spaces -- |g 3.1. |t Introduction -- |g 3.2. |t Definitions and examples -- |g 3.3. |t Basics on open and closed sets -- |g 3.4. |t The subspace topology -- |g 3.5. |t Continuous functions -- |g 4. |t More on open and closed sets and continuous functions -- |g 4.1. |t Introduction -- |g 4.2. |t Basis for a topology -- |g 4.3. |t Limit points -- |g 4.4. |t Interior, boundary and closure -- |g 4.5. |t More on continuity -- |g 5. |t New spaces from old -- |g 5.1. |t Introduction -- |g 5.2. |t Product spaces -- |g 5.3. |t Infinite product spaces (optional) -- |g 5.4. |t Quotient spaces -- |g 5.5. |t Unions and wedges -- |g 6. |t Connected spaces -- |g 6.1. |t Introduction -- |g 6.2. |t Definition, examples and properties -- |g 6.3. |t Connectedness in the real line -- |g 6.4. |t Path-connectedness -- |g 6.5. |t Connectedness of unions and finite products -- |g 6.6. |t Connnectedness of infinite products (optional) -- |g 7. |t Compact spaces -- |g 7.1. |t Introduction -- |g 7.2. |t Definition, examples and properties -- |g 7.3. |t Hausdorff spaces and compactness -- |g 7.4. |t Compactness in the real line -- |g 7.5. |t Compactness of products -- |g 7.6. |t Finite intersection property (optional) |
| 505 | 0 | 0 | |g 8. |t Separation axioms -- |g 8.1. |t Introduction -- |g 8.2. |t Definition and examples -- |g 8.3. |t Regular and normal spaces -- |g 8.4. |t Separation axioms and compactness -- |g 9. |t Metric spaces -- |g 9.1. |t Introduction -- |g 9.2. |t Definition and examples -- |g 9.3. |t Properties of metric spaces -- |g 9.4. |t Basics on sequences -- |g 10. |t The classification of surfaces -- |g 10.1. |t Introduction -- |g 10.2. |t Surfaces and higher-dimensional manifolds -- |g 10.3. |t Connected sums of surfaces -- |g 10.4. |t The classification theorem -- |g 10.5. |t Triangulations of surfaces -- |g 10.6. |t Proof of the classification theorem -- |g 10.7. |t Euler characteristics and uniqueness -- |g 11. |t Fundamental groups and covering spaces -- |g 11. 1. |t Introduction -- |g 11.2. |t Homotopy of functions and paths -- |g 11.3. |t An operation on paths -- |g 11.4. |t The fundamental group -- |g 11.5. |t Covering spaces -- |g 11.6. |t Fundamental group of the circle and related spaces -- |g 11.7. |t The fundamental groups of surfaces -- |t References -- |t Index. |
| 520 | |a 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. | ||
| 546 | |a English. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Algebraic topology. |0 http://id.loc.gov/authorities/subjects/sh85003438. | |
| 650 | 0 | |a Point set theory. |0 http://id.loc.gov/authorities/subjects/sh85057517. | |
| 650 | 7 | |a Algebraic topology. |2 fast |0 (OCoLC)fst00804941. | |
| 650 | 7 | |a Point set theory. |2 fast |0 (OCoLC)fst01068109. | |
| 776 | 0 | 8 | |i Print version: |a Shick, Paul Louis, 1956- |t Topology. |d Hoboken, N.J. : Wiley-Interscience, ©2007 |z 0470096055 |w (DLC) 2006041362 |w (OCoLC)71790194. |
| 830 | 0 | |a Pure and applied mathematics (John Wiley & Sons : Unnumbered) |0 http://id.loc.gov/authorities/names/n42745140. | |
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