Basic Course in 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.