Foundations of Algebraic Topology

Description

The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. Frontmatter -- Preface -- Contents -- I. Axioms and general theorems -- II. Simplicial complexes -- III. Homology theory of simplicial complexes -- IV. Categories and functors -- V. Chain complexes -- VI. Formal homology theory of simplicial complexes -- VII. The singular homology theory -- VIII. Systems of groups and their limits -- IX. The Čech homology theory -- X. Special features of the Čech theory -- XI. Applications to Euclidean Spaces -- Index