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Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points.

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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.


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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 The present book is intended as a bridge from that time to the present.

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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.

Pointless topology

The Categories Loc and Frm 1 Special morphisms. So please proceed with care and consider checking the Crossref privacy policy and the OpenCitations privacy policy.


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    Serie: Frontiers in Mathematics

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