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 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 Source: 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-studytext.'

Peter Johnstone Source: 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 Source: Zentralblatt MATH