Foundations of Combinatorial Topology (Dover Books on Mathematics)

Hailed by The Mathematical Gazette as "an extremely valuable addition to the literature of algebraic topology," this concise but rigorous introductory treatment focuses on applications to dimension theory and fixed-point theorems. The lucid text examines complexes and their Betti groups, including Euclidean space, application to dimension theory, and decomposition into components; invariance of the Betti groups, with consideration of the cone construction and barycentric subdivisions of a complex; and continuous mappings and fixed points. Proofs are presented in a complete, careful, and elegant manner.
In addition to its value as a one-semester text for graduate-level courses, this volume can also be used as a reference in preparing for seminars or examinations and as a source of basic information on combinatorial topology. Although considerable mathematical maturity is required of readers, formal prerequisites are merely a few simple facts about functions of a real variable, matrices, and commutative groups.