A Basic Course in Topology by Gerd Laures

A Basic Course in Topology by Gerd Laures

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.

Prof. Dr. Gerd Laures ist Inhaber des Lehrstuhls Topologie an der Universitat Bochum. Er ist mitverantwortlich fur die Ausbildung der Studierenden in Bachelor- und Masterstudiengangen sowie fur die Doktorandenausbildung. Zuvor war er an den Universitaten Bonn, Heidelberg, Mainz und am M.I.T. in Boston (USA) tatig.

Dr. Markus Szymik hat Mathematik und Philosophie in Gottingen und Bielefeld studiert und ist zurzeitWissenschaftlicher Assistent am Lehrstuhl Topologie in Bochum.