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.
Rezensionen / Stimmen
'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 Kuenzi, Zentralblatt MATH
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Illustrationen
Worked examples or Exercises; 11 Halftones, unspecified; 35 Line drawings, unspecified
Maße
Höhe: 231 mm
Breite: 155 mm
Dicke: 30 mm
Gewicht
ISBN-13
978-1-107-03413-6 (9781107034136)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Jean Goubault-Larrecq is Full Professor of Computer Science at the Ecole Normale Superieure de Cachan, France. He obtained his PhD in 1993 from the Ecole 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.
Autor*in
Ecole Normale Superieure de Cachan
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.
