Topology via Logic: 5 (Cambridge Tracts in Theoretical Computer Science, Series Number 5)
Cambridge University Press
Edition: New Ed, 8/21/2008
EAN 9780521576512, ISBN10: 0521576512
Paperback, 220 pages, 25.9 x 17.3 x 1.3 cm
Language: English
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.