This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.
- The only topology book that covers domain theory (essential for modern computer science)
- Material becomes progressively more advanced to suit both graduate students and experienced researchers
- Includes a variety of more than 450 exercises to challenge readers at every level
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Reviews & endorsements
'The presentation is very well thought out and lively, and the topic selection shows great care on the part of the author. The book will certainly be a very welcome addition to the topological literature … this is certainly topology done well, presented in a highly readable form.' Alexander Yurievich Shibakov, Mathematical Reviews
'It is well written, and profusely (and helpfully) illustrated. The notation is well-chosen, and the numerous exercises are well-integrated into the text, so that it would make a good self-study text.' Peter Johnstone, Bulletin of the London Mathematical Society
'The presentation is highly original … [this] book brings a refreshing perspective to topology … the material has obviously been chosen with great care and the book is very well written.' Hans-Peter Künzi, Zentralblatt MATH
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Product details
- Date Published: March 2013
- format: Hardback
- isbn: 9781107034136
- length: 497 pages
- dimensions: 235 x 157 x 28 mm
- weight: 0.82kg
- contains: 46 b/w illus. 485 exercises
- availability: Available
Table of Contents
1. Introduction
2. Elements of set theory
3. A first tour of topology: metric spaces
4. Topology
5. Approximation, and function spaces
6. Metrics, quasi-metrics, hemi-metrics
7. Completeness
8. Sober spaces
9. Stably compact spaces, and compact pospaces
References
Notation index
Index.
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Author
Jean Goubault-Larrecq, Ecole Normale Supérieure de Cachan
Jean Goubault-Larrecq is Full Professor of Computer Science at the École Normale Supérieure de Cachan, France. He obtained his PhD in 1993 from the École Polytechnique in the field of automated deduction, and since then he has led an active career in several fields of computer science: logic, computer security, semantics, domain theory, probabilistic and non-deterministic systems. He is currently heading team SECSI (security of information systems) at INRIA, France's national institute for research in computer science and control. He is the recipient of the 2011 CNRS Silver Medal in the field of computer science and its interactions. This is the highest scientific distinction in computer science in France.