Book:Peter T. Johnstone/Stone Spaces

Peter T. Johnstone: Stone Spaces

Published $\text {1982}$, Cambridge University Press

ISBN 0-521-33779-8

Subject Matter

• Stone spaces

Contents

Preface

Advice to the reader

Introduction: Stone's Theorem in historical perspective

I$\quad$Preliminaries

1$\quad$Lattices

2$\quad$Ideals and filters

3$\quad$Some categorical concepts

4$\quad$Free lattices

$\,\,\,\quad$Notes on chapter I

II$\quad$Introduction to locales

1$\quad$Frames and locales

2$\quad$Sublocales and sites

3$\quad$Coherent locales

4$\quad$Stone spaces

$\,\,\,\quad$Notes on chapter II

III$\quad$Compact Hausdorff spaces

1$\quad$Compact regular locales

2$\quad$Manes' Theorem

3$\quad$Gleason's Theorem

4$\quad$Vietoris locales

$\,\,\,\quad$Notes on chapter III

IV$\quad$Continuous real-valued functions

1$\quad$Complete regularity and Urysohn's Lemma

2$\quad$The Stone-Čech compactification

3$\quad\map C X$ and $\map {C^*} X$

4$\quad$Gelfand duality

$\,\,\,\quad$Notes on chapter IV

V$\quad$Representations of rings

1$\quad$A crash course in sheaf theory

2$\quad$The Pierce spectrum

3$\quad$The Zariski spectrum

4$\quad$Ordered rings and real rings

$\,\,\,\quad$Notes on chapter V

VI$\quad$Profiniteness and duality

1$\quad$Ind-objects and pro-objects

2$\quad$Profinite sets and algebras

3$\quad$Stone-type dualities

4$\quad$General concrete dualities

$\,\,\,\quad$Notes on chapter VI

VII$\quad$Continuous lattices

1$\quad$Compact topological (semi)lattices

2$\quad$Continuous posets and lattices

3$\quad$Lawson semilattices

4$\quad$Locally compact locales

$\,\,\,\quad$Notes on chapter VII

Bibliography

Index of categories

Index of other symbols

Index of definitions