Overview
- Offers a modern presentation of the most important terms and ideas in topology
- Includes a variety of examples, illustrations, and exercises
- Can be used for self-study
Part of the book series: Compact Textbooks in Mathematics (CTM)
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About this book
This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects. It is designed as a bridge between elementary courses in analysis and linear algebra and more advanced classes in algebraic and geometric topology, making it particularly suitable for both undergraduate and graduate mathematics students. Additionally, it can be used for self-study.
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.
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Table of contents (11 chapters)
Authors and Affiliations
About the authors
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.
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Bibliographic Information
Book Title: A Basic Course in Topology
Authors: Gerd Laures, Markus Szymik
Series Title: Compact Textbooks in Mathematics
DOI: https://doi.org/10.1007/978-3-662-70602-2
Publisher: Birkhäuser Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2025
Softcover ISBN: 978-3-662-70601-5Published: 15 February 2025
eBook ISBN: 978-3-662-70602-2Published: 14 February 2025
Series ISSN: 2296-4568
Series E-ISSN: 2296-455X
Edition Number: 1
Number of Pages: XII, 245
Number of Illustrations: 182 b/w illustrations
Topics: Algebraic Geometry, Algebraic Topology