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.

• Algebraic Topology
• Homotopy
• Categories
• Compactness
• Set-Theoretic Topology

• Front Matter
• Basic Concepts of Topology
• Universal Constructions
• Connectivity and Separation
• Compactness and Mapping Spaces
• Transformation Groups
• Paths and Loops
• Fundamental Groups
• Covering Spaces
• Bundles and Fibrations
• Sheaves
• Simplicial Sets
• Back Matter

Gerd Laures

Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany

Markus Szymik

School of Mathematical and Physical Sciences, University of Sheffield, Sheffield, UK

Book Title：A Basic Course in Topology

Book Subtitle：/

Authors：Gerd Laures, Markus Szymik

DOI：https://doi.org/10.1007/978-3-662-70602-2

eBook Packages：Mathematics and Statistics, Mathematics and Statistics (R0)

Edition Number：1

Number of Pages：XII, 245

Number of Illustrations：182 b/w illustrations

Topics:Algebraic Geometry, Algebraic Topology