Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics) 1997th Edition by Gerard Buskes (PDF)

Description

gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections – The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of “Extras” at the end of each chapter presenting a brief foray outside topology.

User’s Reviews

Editorial Reviews: Review This is a gentle introduction to topological spaces leading the reader to understand the notion of what is important in topology vis-a-vis geometry and analysis. The authors have carefully divided the book into three sections; The line and the plane, Metric spaces and Topological spaces, in order to mitigate the move into higher levels of abstraction. Students are thereby informally assisted in getting aquainted with new ideas while remaining on familiar territory. The authors have also restricted the mathematical vocabulary in the book to avoid overwhelming the reader with the extensive array of technical terms indicating the properties of topological spaces. Additionally, the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. — Book Description

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

⭐I’m a graduate student in mathematics and this is one of the few math books I can highly recommend. Topological concepts are made intuitive, so when you get to the formal definitions, they are no surprise, you even expect them. Sometimes it is explained why a ‘seemingly obvious solution’ doesn’t work after all. This really helps you to see WHY things are done the way they are. After reading this book you’ll have a good basic understanding of what topology is all about. With this background it should be no problem to tackle more advanced texts on topology.By the way, I love the ‘Extras’ in the book. They are little pieces of history or excursions into other parts of mathematics that can be found at the end of each chapter.

⭐It starts the discussion with the familiar metric spaces and the real line and thenshows how convergence can be generalized. From this point, he then shows theconnection to topology. He also provides motivation for the results, exercises,and historical sketches at the end of every chapter. The writing is unusuallyclear.

⭐There are enough examples and explanations of such sheer brilliance that one can forgive the occasional lapse. I particularly enjoyed the following:(1) the Hilbert space-filling curve, and homeomorphic sets in chapter 4;(2) all of chapter 5 on ‘Metrics’, and especially the example of an ‘unorthodox metric’ on p91;(3) all of chapter 8 on ‘Uniform Convergence’, the opening section of which is so simple, and stunningly instructive and entertaining, that it could be used in the school classroom;(4) the “Extra” section on p-adic numbers in chapter 9. It is here that the book worked its magic, by leading me to buy another book in order to study these astonishing numbers in detail;(5) the section on ‘Quotient Spaces’ in chapter 14.There are a few misprints, but these are for the most part obvious to the attentive reader, and should cause no problem.I was perplexed by the authors’ reference to a “sharp” angle (page 68) in the section on Brouwer’s Theorem, and the subsequent 4 pages could do with tidying up with regard to notation and typos. A more serious instance of sloppiness appears on page 302, where, in an attempt to impress upon the reader the monstrosity of the set of real numbers, it is stated, “If you own as many dollars as there are real numbers, you may lose an infinite amount of money and you will never know the difference”. Well, what if you own merely a countably infinite number of dollars! This lapse was, however, surprising and very atypical.I was dismayed to read one other review, in which the book was denigrated. It is easy to find fault. In truth, despite a small number of glitches, the book makes the subject beautiful, and overall it is a tour de force in didactic technique. This merits the 5 star rating.

⭐Ich habe das Buch wegen der guten Bewertungen gekauft. Ich finde das Buch aber langweilig und für Einsteiger didaktisch schlecht aufgebaut. Dies merkt man bereits beim Layout. Die Themen sind eher überladen. Es gibt ein paar interessante Aufgaben, aber ich würde eher empfehlen, eines der Standardwerke zu kaufen.Excellent book for those making the transition to abstract mathematics.I am a Ph.D candidate in Economics and I feel that this book has contributed to my mathematical maturity.

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Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics) 1997th Edition PDF Free Download
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Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics) 1997th Edition 1997 PDF Free Download
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