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Frames and Locales: Topology Without Points Jorge Picado

Frames and Locales: Topology Without Points

Jorge Picado

Published October 22nd 2011
ISBN : 9783034801539
Paperback
398 pages
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 About the Book 

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 placeMoreUntil 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 onchoice principles became constructive. The result is often a smoother, rather than a more entangled, theory.No monograph of this nature has appeared since Johnstones 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.