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.
Dover (2015) republication of the edition originally published by the Graylock Press, Rochester, New York, 1952, and reprinted by Dover Publications, Inc., in 1999.
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