Non-Hausdorff Topology and Domain Theory

Selected Topics in Point-Set Topology
Erscheinungsjahr 2013
ISBN: 978-1-107-03413-6
Verlag: Cambridge University Press

Buch, Englisch, Band 22, 497 Seiten, Format (B × H): 155 mm x 231 mm, Gewicht: 816 g

Reihe: 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.

Autoren/Hrsg.

Goubault-Larrecq, Jean

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik

Inhaltsverzeichnis

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.

Über Autor(innen)

Goubault-Larrecq, Jean
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.