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Topology Via Logic

1989 Computers
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Release : 1989
Genre : Computers
Kind : eBook
Book Rating : 512/5 ( reviews)

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Book Synopsis Topology Via Logic by : Steven Vickers

Download or read book Topology Via Logic written by Steven Vickers. This book was released on 1989. Available in PDF, EPUB and Kindle. Book excerpt: Now 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.

Experiments in Topology

2012-12-04 Mathematics
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Release : 2012-12-04
Genre : Mathematics
Kind : eBook
Book Rating : 74X/5 ( reviews)

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Book Synopsis Experiments in Topology by : Stephen Barr

Download or read book Experiments in Topology written by Stephen Barr. This book was released on 2012-12-04. Available in PDF, EPUB and Kindle. Book excerpt: Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

Frames and Locales

2011-10-21 Mathematics
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Release : 2011-10-21
Genre : Mathematics
Kind : eBook
Book Rating : 548/5 ( reviews)

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Book Synopsis Frames and Locales by : Jorge Picado

Download or read book Frames and Locales written by Jorge Picado. This book was released on 2011-10-21. Available in PDF, EPUB and Kindle. Book excerpt: Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent. Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory. No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.

Topology of Tiling Spaces

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 279/5 ( reviews)

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Book Synopsis Topology of Tiling Spaces by : Lorenzo Adlai Sadun

Download or read book Topology of Tiling Spaces written by Lorenzo Adlai Sadun. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces." "The text contains a generous supply of examples and exercises."--BOOK JACKET.

Topology

2020-08-18 Mathematics
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Release : 2020-08-18
Genre : Mathematics
Kind : eBook
Book Rating : 626/5 ( reviews)

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Book Synopsis Topology by : Tai-Danae Bradley

Download or read book Topology written by Tai-Danae Bradley. This book was released on 2020-08-18. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

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