Horst Herrlich Bücher

This is a by now classical text in mathematics. It gives an introduction to category theory assuming only minimal knowledge in set theory, algebra or topology. The book is designed for use during the early stages of graduate study -- or for ambitious undergraduates. Each chapter contains numerous exercises for further study and control. The attempt is made to present category theory mainly as a convenient language -- one which ties together widespread notions, which puts many existing results in their proper perspective, and which provides a means for appreciation of the unity that exists in modern mathematics, despite the increasing tendencies toward fragmentation and specialization. The fact that the book appears in a 3rd edition proves that the authors achieved their goals.

AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that: - Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC). - Disasters happen with AC: Many undesirable mathematical monsters are being created (e. g., non measurable sets and undeterminate games). - Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e. g., by AD, the axiom of determinateness). Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.