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.