General Topology by J. Dixmier (PDF)

Description

I Topological Spaces.- II Limits. Continuity.- III Constructions of Topological Spaces.- IV Compact Spaces.- V Metric Spaces.- VI Limits of Functions.- VII Numerical Functions.- VIII Normed Spaces.- IX Infinite Sums.- X Connected Spaces.- Exercises.- Index of Notations.- Index of Terminology.

User’s Reviews

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

⭐Very clear, well written, short, and rigorous. Worth every penny and recommended for PhD students who need to use these tools but don’t have the time to read and understand one of the “comprehensive” texts.

⭐This book is really good. Thanks

⭐This is a quite good book on general topology concentrated on topics relevant for getting deeper and better understanding of more advanced analysis. It is very short but still informative with a lot of well chosen facts, examples and comparisons. The way the material is presented is impressive. I like the way definitions are put in the text: first a theorem stating that several assertions are equivalent and then a definition bringing a notion based on the assertions of the theorem. Thus the reader readily gets a better picture of the just defined term that actually gets presented in several ways at once. There also are other good sides of the text.

⭐This is an oustanding book on introductory topology (point set topology). The book is short and the author does not get into basic algebraic topology as Munkres, for example, does. However, it is solid and complete and the proofs presented by Dixmier are surprisingly optimised: very concise but always clear. Not only is this convenient while studying from it, but the style is also a model on how one should write one’s proofs.For those able to read mathematics in French, I’d strongly recommend the original version, if available.

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