Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition.
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Text: English (translation)
Original Language: French
Original Language: French
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12 of 13 people found the following review helpful:
5.0 out of 5 stars
A classic text.,
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This review is from: Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics) (Paperback)
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.
5.0 out of 5 stars
Great!,
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This review is from: Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics) (Paperback)
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.
3 of 5 people found the following review helpful:
3.0 out of 5 stars
It is one clear exposition of very much subjects,
By R. Cardoso (Portugal) - See all my reviews
This review is from: Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics) (Paperback)
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.
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