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Topology via Logic (Cambridge Tracts in Theoretical Computer Science) [Paperback]

Steven Vickers
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

September 13, 1996 0521576512 978-0521576512
This advanced textbook on topology 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 author freely exploits the methods of locale theory. Third, there is substantial discussion of some computer science applications. 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 for computer scientists.

Editorial Reviews

Book Description

This is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.

Product Details

  • Series: Cambridge Tracts in Theoretical Computer Science (Book 5)
  • Paperback: 220 pages
  • Publisher: Cambridge University Press (September 13, 1996)
  • Language: English
  • ISBN-10: 0521576512
  • ISBN-13: 978-0521576512
  • Product Dimensions: 10.2 x 6.7 x 0.4 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #2,070,297 in Books (See Top 100 in Books)

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18 of 19 people found the following review helpful
By A Customer
This is a very accessible account relating the theory of locales to classical point set topology, with remarks along the way about the relation between the two theories in terms of category theory.
Locales are lattices, which also have all joins of arbitrary subsets, just as topologies also have finite intersections of open sets and arbitrary unions; finite meets also distribute over arbitrary joins.
In locale theory, you can do topology without using points (the art of "pointless thinking", as Johnstone likes to call it), although you can also introduce points in locales by definition.
Locales, in other words, are complete lattices, and their elements can be identified with open sets. In the other direction, "points" in locales (which can be identified with principal prime ideals) correspond to the points in a corresponding topological space.
The book is a nice introduction to Johnstone's now classic *Stone Spaces*. But the "logic&qu! ot; as in *Topology via Logic*-- refers to "logic" in the sense of computer science. Readers at home with symbolic logic may therefore find the examples, all based on "data streams" of bits, a bit strange, and may want to translate them into more familiar terms. But the reward is worth the effort.
The informal style and free use of pictures to illustrate ideas is also a refreshing, and welcome change from the rigid and unnecessarily formal style too often encountered in books on this and similar topics.
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2 of 2 people found the following review helpful
By Subrata
Format:Paperback|Verified Purchase
The book Topology via Logic (Cambridge Tracts in Theoretical Computer Science) by Steven Vickers is the only book that I found a nice bridge between the abstract Topological theory and the general life reasoning. This not only a wonderful book for a Computer Scientists it is also a great book for Set Theoretic Topologists and Logicians who are always dealing with modelling natural language/incomplete knowledge etc. I found it is the best book to helping my research in incomplete information system with the the abstract Topological Theories.
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