Book:Peter T. Johnstone/Stone Spaces

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