Shick Topology

Point-Set and Geometric
1. Auflage 2011
ISBN: 978-1-118-03058-5
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 296 Seiten, E-Book

Reihe: Wiley Series in Pure and Applied Mathematics

The essentials of point-set topology, complete with motivation andnumerous examples
Topology: Point-Set and Geometric presents an introduction totopology that begins with the axiomatic definition of a topology ona set, rather than starting with metric spaces or the topology ofsubsets of Rn. This approach includes many more examples, allowingstudents to develop more sophisticated intuition and enabling themto learn how to write precise proofs in a brand-new context, whichis an invaluable experience for math majors.
Along with the standard point-set topologytopics--connected and path-connected spaces, compact spaces,separation axioms, and metric spaces--Topology covers theconstruction of spaces from other spaces, including products andquotient spaces. This innovative text culminates with topics fromgeometric and algebraic topology (the Classification Theorem forSurfaces and the fundamental group), which provide instructors withthe opportunity to choose which "capstone" best suits his or herstudents.
Topology: Point-Set and Geometric features:
* A short introduction in each chapter designed to motivate theideas and place them into an appropriate context
* Sections with exercise sets ranging in difficulty from easy tofairly challenging
* Exercises that are very creative in their approaches and workwell in a classroom setting
* A supplemental Web site that contains complete and colorfulillustrations of certain objects, several learning modulesillustrating complicated topics, and animations of particularlycomplex proofs

Autoren/Hrsg.

Shick, Paul L.

Inhaltsverzeichnis

Foreword.
Acknowledgments.
1. Introduction: Intuitive Topology.
2. Background on Sets and Functions.
3. Topological Spaces.
4. More on Open and Closed Sets and Continuous Functions.
5. New Spaces from Old.
6. Connected Spaces.
7. Compact Spaces.
8. Separation Axioms.
9. Metric Spaces.
10. The Classification of Surfaces.
11. Fundamental Groups and Covering Spaces.
References.
Index.

Über Autor(innen)

PAUL L. SHICK, PhD, is Professor in the Department of Mathematics and Computer Science at John Carroll University in Cleveland, Ohio. He earned a PhD in Mathematics from Northwestern University in 1984, working in the area of stable homotopy theory. He remains active in research in algebraic topology.