Non-Hausdorff Topology and Domain Theory

Selected Topics in Point-Set Topology

Jean Goubault-Larrecq (Ecole Normale Supérieure de Cachan)

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English

Cambridge University Press
28 March 2013

Topology

Series: New Mathematical Monographs

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.

By: Jean Goubault-Larrecq (Ecole Normale Supérieure de Cachan)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 22
Dimensions: Height: 235mm, Width: 157mm, Spine: 28mm
Weight: 820g
ISBN: 9781107034136
ISBN 10: 1107034132
Series: New Mathematical Monographs
Pages: 497
Publication Date: 28 March 2013
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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.

Reviews for Non-Hausdorff Topology and Domain Theory: Selected Topics in Point-Set Topology

'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 Kunzi, Zentralblatt MATH