Topology via Logic

This is an advanced textbook on topology for computer scientists.

Steven Vickers (Author)

9780521576512, Cambridge University Press

Paperback, published 22 August 1996

220 pages, 43 b/w illus. 64 exercises
26 x 17.2 x 1.3 cm, 0.57 kg

Now in paperback, Topology via Logic is an advanced textbook on topology for computer scientists. Based on a course given by the author to postgraduate students of computer science at Imperial College, it has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the methods of locale theory are freely exploited. Third, there is substantial discussion of some computer science applications. Although books on topology aimed at mathematics exist, no book has been written specifically for computer scientists. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap.

1. Introduction
2. Affirmative and refutative assertions
3. Frames
4. Frames as algebras
5. Topology: the definitions
6. New topologies for old
7. Point logic
8. Compactness
9. Spectral algebraic locales
10. Domain theory
11. Power domains
12. Spectra of rings
Bibliography.

Subject Areas: Mathematical theory of computation [UYA], Mathematical logic [PBCD]