A Basic Course in Topology

Erscheinungsjahr 2025
ISBN: 978-3-662-70601-5
Verlag: Springer

Buch, Englisch, 245 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 400 g

Reihe: Compact Textbooks in Mathematics

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Szymik, Markus

Laures, Gerd

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

- 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.

Über Autor(innen)

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.