A Basic Course in Topology
Springer-Verlag
978-3-662-70601-5 (ISBN)
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The authors employ the modern language of category theory to unify and clarify the concepts presented, with definitions supported by numerous examples and illustrations. The book includes over 170 exercises that reinforce and deepen the understanding of the material. Many sections feature brief insights into advanced topics, providing a foundation for study projects or seminar presentations.
In addition to set-theoretic topology, the book covers essential concepts such as fundamental groups, covering spaces, bundles, sheaves, and simplicial methods, which are vital in contemporary geometry and topology.
Gerd Laures holds the Chair of Topology at the University of Bochum. He is jointly responsible for the education of students in bachelor’s and master’s programs, as well as for doctoral training. Previously, he worked at the universities of Bonn, Heidelberg, Mainz, and at MIT in Boston (USA). Markus Szymik holds a Chair of Pure Mathematics at the University of Sheffield. He studied mathematics and philosophy at the universities of Göttingen and Bielefeld and has done research at various other institutions at Bochum, Bonn, Cambridge, Copenhagen, Düsseldorf, Harvard, MIT, NTNU, Oxford, Stanford, and Stockholm. His research focuses on algebraic and geometric problems related to symmetries.
- Basic Concepts of Topology.- Universal Constructions.- Connectivity and Separation.- Compactness and Mapping Spaces.- Transformation Groups.- Paths and Loops.- The Fundamental Group.- Covering Spaces.- Bundles and Fibrations.- Sheaves.- Simplicial Sets.
| Erscheint lt. Verlag | 22.2.2025 |
|---|---|
| Reihe/Serie | Compact Textbooks in Mathematics |
| Zusatzinfo | 164 Illustrations, black and white; X, 250 p. 164 illus. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 3-662-70601-6 / 3662706016 |
| ISBN-13 | 978-3-662-70601-5 / 9783662706015 |
| Zustand | Neuware |
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