Description

Book Synopsis
Over the last 45 years, Boolean theorem has been generalized and extended in several different directions and its applications have reached into almost every area of modern mathematics; but since it lies on the frontiers of algebra, geometry, general topology and functional analysis, the corpus of mathematics which has arisen in this way is seldom seen as a whole. In order to give a unified treatment of this rather diverse body of material, Dr Johnstone begins by developing the theory of locales (a lattice-theoretic approach to 'general topology without points' which has achieved some notable results in the past ten years but which has not previously been treated in book form). This development culminates in the proof of Stone's Representation Theorem.

Table of Contents
Preface; Advice to the reader; Introduction; 1. Preliminaries; 2. Introduction to locales; 3. Compact Hausdorff spaces; 4. Continuous real-valued functions; 5. Representations of rings; 6. Profiniteness and duality; 7. Continuous lattices; Bibliography; Index of categories; Index of other symbols; Index of definitions.

Stone Spaces 3 Cambridge Studies in Advanced Mathematics Series Number 3

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    A Paperback by Peter T. Johnstone

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      View other formats and editions of Stone Spaces 3 Cambridge Studies in Advanced Mathematics Series Number 3 by Peter T. Johnstone

      Publisher: Cambridge University Press
      Publication Date: Publication Date: 8/14/1986 12:00:00 AM
      ISBN13: 9780521337793, 978-0521337793
      ISBN10: 0521337798
      Also in:
      Geometry Mathematical foundations

      Description

      Book Synopsis
      Over the last 45 years, Boolean theorem has been generalized and extended in several different directions and its applications have reached into almost every area of modern mathematics; but since it lies on the frontiers of algebra, geometry, general topology and functional analysis, the corpus of mathematics which has arisen in this way is seldom seen as a whole. In order to give a unified treatment of this rather diverse body of material, Dr Johnstone begins by developing the theory of locales (a lattice-theoretic approach to 'general topology without points' which has achieved some notable results in the past ten years but which has not previously been treated in book form). This development culminates in the proof of Stone's Representation Theorem.

      Table of Contents
      Preface; Advice to the reader; Introduction; 1. Preliminaries; 2. Introduction to locales; 3. Compact Hausdorff spaces; 4. Continuous real-valued functions; 5. Representations of rings; 6. Profiniteness and duality; 7. Continuous lattices; Bibliography; Index of categories; Index of other symbols; Index of definitions.

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