Book:Peter T. Johnstone/Stone spaces

From ProofWiki
Jump to navigation Jump to search

Peter T. Johnstone: Stone spaces

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

ISBN 0-521-33779-8.


Subject Matter


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