Customer Reviews

Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics)

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Claude Berge's Topological Spaces is a classic text that deserves to be in the libraries of all mathematical economists. It contains many of the fundamental underpinnings of modern mathematical economics. This book has been long out of print and its reprinting by Dover is very welcome. Readers who find this book of interest should also look at Dover's edition of Samuel Karlin's two volume book on mathematical programming and games that has been reprinted as a single volume.

This is a wonderful book. I don't believe that it should be your first book in topology. But for sure it will help you to get a deep understanding.

To me, this book has the following questions:

- The definition of the entities that appear in the theorems are not precisely defined, what obliges to extract from the proof of very much theorems the exact meaning of some symbols.

- In the proofs there are very much steps thar are 'giant steps'. Usually the author don't reference the theorems and inequalities used in the proofs.

- Also, some symbols coincide, what obliges to extract from the reasoning the exact meaning of few symbols. For example, -G may mean the complement of the set G, or the symmetric of the set G in one numerical space.

However, the book has very much good aspects, like:

- It covers with some detail one great quantity of subjects in only 263 pages, like topological questions, multi-valued mappings, semi-continuity, convexity, symplexes, extremum problems, and very much more. The subjects usually are very interesting and useful.

- The definitions of the main entities analyzed in each paragraph are easy and intuitive.

- The examples are very well chosen, and present very well the problems to study.

- The book is well organized.

Although this is so much better than the other Dover book by R. Vaidyanathaswamy, I can't say that it is the best topology text that I have read or the best reference, but it covers topics from Banach spaces to functional topology in a pretty readable manner and it is fairly inexpensive!