Using the Borsuk-Ulam theorem: lectures on topological methods in combinatorics and geometry

Jiri Matousek, A. Björner, G.M. Ziegler3540003622, 978-3-540-00362-5

The textbook explains elementary but powerful topological methods based on the Borsuk-Ulam theorem and its generalizations. It covers many substantial results, sometimes with proofs simpler than those in the original papers. At the same time, it assumes no prior knowledge of algebraic topology, and all the required topological notions and results are gradually introduced. History, additional results, and references are presented in separate sections.