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Author: Jean Goubault-Larrecq
Publisher: Cambridge University Press
Published: 2013-03-28
Total Pages: 499
ISBN-13: 1107034132
DOWNLOAD EBOOKIntroduces the basic concepts of topology with an emphasis on non-Hausdorff topology, which is crucial for theoretical computer science.
Author: Jean Goubault-Larrecq
Publisher: Cambridge University Press
Published: 2013-03-28
Total Pages: 499
ISBN-13: 1107328772
DOWNLOAD EBOOKThis 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.
Author: Mai Gehrke
Publisher: Cambridge University Press
Published: 2024-02-29
Total Pages: 370
ISBN-13: 1009349716
DOWNLOAD EBOOKIntroducing Stone–Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
Author: Paul Bracken
Publisher: BoD – Books on Demand
Published: 2023-08-02
Total Pages: 218
ISBN-13: 1837695598
DOWNLOAD EBOOKTopology remains an active and fundamental area of research that plays a foundational role in many branches of mathematics and science, such as analysis, differential geometry, physics and even biology. It is hoped the papers in this book will contribute to stimulating research in this basic area of mathematics.
Author: Erika Ábrahám
Publisher: Springer Nature
Published: 2023-12-24
Total Pages: 451
ISBN-13: 3031479637
DOWNLOAD EBOOKThis book constitutes the proceedings of the 20th International Colloquium on Theoretical Aspects of Computing, ICTAC 2023, which took place in Lima, Peru, during December 4–8, 2023. The 20 full papers presented in this volume together with 3 invited papers and 1 tool paper were carefully reviewed and selected from 40 submissions. They were organised in the topical sections as follows: Bring Together Practitioners; Researchers from Academia; Industry; Government to Present Research Results and Exchange Experience and Ideas.
Author: Mário S. Alvim
Publisher: Springer Nature
Published: 2019-11-04
Total Pages: 485
ISBN-13: 3030311759
DOWNLOAD EBOOKThis Festschrift was published in honor of Catuscia Palamidessi on the occasion of her 60th birthday. It features 6 laudations, which are available in the front matter of the volume, and 25 papers by close collaborators and friends. The papers are organized in topical sections named: concurrency; logic and constraint programming; security and privacy; and models and puzzles. These contributions are a tribute to Catuscia Palamidessi’s intellectual depth, vision, passion for science, and tenacity in solving technical problems. They also reflect the breadth and impact of her work. Her scientific interests include, in chronological order, principles of programming languages, concurrency theory, security, and privacy.
Author: Steven Vickers
Publisher: Cambridge University Press
Published: 1989
Total Pages: 224
ISBN-13: 9780521576512
DOWNLOAD EBOOKNow in paperback, Topology via Logic is an advanced textbook on topology for computer scientists. Based on a course given by the author to postgraduate students of computer science at Imperial College, it has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the methods of locale theory are freely exploited. Third, there is substantial discussion of some computer science applications. Although books on topology aimed at mathematics exist, no book has been written specifically for computer scientists. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap.
Author: Steven G. Krantz
Publisher: MAA
Published: 2009-09-24
Total Pages: 128
ISBN-13: 9780883853467
DOWNLOAD EBOOKA concise introduction to topology to ground students in the basic ideas and techniques of the subject.
Author: Szymon Dolecki
Publisher: World Scientific
Published: 2024-01-03
Total Pages: 733
ISBN-13: 9811232121
DOWNLOAD EBOOKTopological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book — from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
Author: Vasco Brattka
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2014-09-04
Total Pages: 424
ISBN-13: 1614518041
DOWNLOAD EBOOKPublished in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.
