Stone Spaces (Cambridge Studies in Advanced Mathematics, Series Number 3) by Peter T. Johnstone (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is well-known for being difficult. I recommend to have access to other resources. What makes this book uniquely valuable in my experience is the following. Each time I was able to understand one of the chapters, which always took me many detours via other sources, I found that Johnstone’s book had the shortest and most insightful proofs. Moreover, the sections about history and references are a treasure trove of articles most of which would have been forgotten by now without the care the author took to appreciate other people’s work.

⭐I bought this book to try to understand something of the Stone topology. Although this sounds like an obscure subject, the Stone topology is a way of giving a well understood limit structure to set algebras (and thus to algebraic structures in analysis), which is a very rich area. I confess though that I could not get on with this book. The category theoretic approach employed left me cold, and I was not sure of the value of the results achieved. I keep Stone spaces on my book shelf for reference, but I could not in truth recommend it for any other purpose. Of course it could simply be too deep for me …

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