Books in the North-Holland Mathematical Library series

Provides coverage of function spaces of low Borel complexity. This book collects knowledge about general topology. It contains exercises which aim to test the reader's understanding of the material, supply proofs of statements that are used in the text and provide additional information.

Provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This book is useful for graduates and researchers in both algebra and logic.

Focuses on cross-fertilisations between stream ciphers and number theory. This work covers known connections between the two areas. It contains over thirty research problems for stimulating interactions between the two areas. It is written by leading researchers in stream ciphers and number theory.

General concepts and methods that occur throughout mathematics - and now also in theoretical computer science - are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further. The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi. A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.