Book:Peter T. Johnstone/Stone Spaces
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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