Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal. Introduction to Topology has ratings and 15 reviews. Steve said: I’m not yet enough of an expert on topology to give this a truly informed review; I. This book is meant to cover a basic topology course for undergraduates and I found it very approachable even with my limited background in pure math.
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Introduction to Topology
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Refresh introdutcion try again. Open Preview See a Problem? Thanks for telling us about the problem. Return to Book Page. Preview — Introduction to Topology by Bert Mendelson. Introduction to Topology by Bert Mendelson. PaperbackThird Editionpages. Published July 1st by Dover Publications first published January 1st To see what your friends thought of this book, please sign up. To ask other readers questions about Introduction to Tpologyplease sign up.
Be the first to ask a question about Introduction to Topology. Lists with This Book. Sep 14, Steve Stuart rated it really liked it. I’m not yet enough of an expert on topology to give this a truly informed review; I can compare this to only to one intdoduction topology text but plenty of math books. The book starts out with a very compact review of set theory no pun intended.
Then comes a warmup chapter on metric spaces, which seems a bit cumbersome in places, but is turns out to be carefully designed to use exactly the same structure as will be used when introducing similar topics for topological spaces. The tour through metric I’m not yet enough of an topoloty on topology to give this a truly informed review; I can compare this to only to one other topology text but plenty of math books.
The tour through metric spaces is quite helpful, introducing abstract definitions of topics such as continuity, neighborhoods and limit points that are crucial in topological spaces while the reader still has the crutch of distances to fall back on to make sense of the concepts.
The topology content covered is entirely point-set topology, covering the basics of openness, compactness, and connectedness, without moving any deeper. The book is very self-contained, and should be accessible to any undergrad iintroduction with proofs and preferably at least some exposure to real analysis. That’s not to say reading it is ingroduction, however; expect to put in some work following the proofs and solving problems if you want to get something out of it. The style of the book is quite elegant and spare.
It doesn’t elaborate once an argument or proof is complete, but is ihtroduction readable despite its terseness. This style will be too brief for students who want more redundancy, hand-holding, and worked exercises. But it’s quite enjoyable for those who are willing and able to supply the mental effort and let the author guide your efforts. The book includes plenty of to;ology examples, of a range of difficulties.
Working a sampling of these after each section is plenty to ensure that you have understood the material. One thing I would have appreciated, though, is a few more examples of non-Euclidean topological spaces that I could vert used as exercises to poke at the definitions and proofs. My intuition is still embedded way too deeply in Euclidean space, and I have to stress-test it to know when I’m relying on it too tk.
Some of the terminology used is slightly non-standard, or out-of-date. The theorems never change, but the wording does, slowly, and this is visible when Mendelson uses terms like identification topology rather than quotient space. This makes it slightly more inconvenient to match topics when supplementing this text with other sources or vice versa, but I suppose this is inevitable in a book that was first published topilogy than 50 mende,son ago.
Texts in fields other than math tend to become dated much faster.
Introduction to Topology: Third Edition
The best part about the book is the price. Dover editions are nearly always a bargain, and this one is no exception. Sep 06, CD rated it really liked it Shelves: I actually have the Second Edition, must speak with a librarian or become one to add this and several other ‘older’ books of this standard.
Not unlike several other ‘Intro’ books, there is a rather large amount of pre-req knowledge required. If you are firmly rooted in your understanding of Set Theory and have had rigorous levels of experience with that nomenclature, only the first couple of readings will be a muddle.
One of the best formal introductions to basic Topology. If you are studying a I actually have the Second Edition, must speak with a librarian or become one to add this and several other ‘older’ books of this standard. If you are studying any of the modern flashback theories of the universe, the relationship between Hilbert Space and Euclidean inclusion along convergences is a must! A little dense initially on the important topic of convergence, but you will get there more quickly than with most other elaborations that I know of up to books even as recent as years ago circa This is basic stuff folks!
Get it right the first time and your wonderment over dimensionality will become a diminishing metric subspace oops, another obscure application of Topology and not intro level. Jun 02, Billy Dean rated it liked it.
You caught me–technically, I haven’t finished this book yet. I’ll admit that I’m not quite ready to tackle topology itself. However, the introductory overview of set theory and set theoretical notation is invaluable if you’re interested at all in foundational mathematics or philosophy of mathematics be it Russell or Badiou. I had worn myself out on other books dedicated to the subject, and this book provides a clearer, more to-the-point account of basic set theory than any I’ve found in a fi You caught me–technically, I haven’t finished this book yet.
I had worn myself out on other books dedicated to the subject, and this book provides a clearer, more to-the-point account of basic set theory than any I’ve found in a fifty page introduction, no less!
In this regard, it’s worth the read.
Introduction to Topology: Third Edition
I’ll get back to you about the rest when I’m more prepared to treat topology in earnest. Jul 11, Jason Evans rated it liked it. Good lord I hate topology. Good book on it, though. Aug 14, Chandra Prakash rated it really liked mendelzon. This is my first book on Topology, and it’s quite good. First few chapters are basic and about sets, functions. The nest thing I liked about this book was that it connected the topics connectedness to intermediate value theorem and as such.
It was sort of helpful in getting the big picture of Topology and its relationship to calculus and other branch of Mathematics. Great Book to start studying Topology. Jun 28, Simona Vesela rated it it was amazing Shelves: It has taken me roughly 20 hours to read the first 40 pages.
That was 4 years ago. Last few weeks I have worked through the rest in maybe 10 hours. What made this book stand out for me back then eas, that it was very indroductory and didn’t assume much. The exercises have tlpology the material and have been fun to work through. Sep 19, James rated it liked it.
Good book but very dense for a non-mathematician like myself. Doesn’t really help one mendeleon an intuition of the subject. Dec 18, Guillermo Angeris rated it it was amazing Shelves: Overall, great introductory book to topology. The pedagogy was excellent and the development of topics made sense in going from metric spaces a notion that is generally more intuitive to abstract topological spaces.
In particular, inttoduction was great for self-study as Mendelson doesn’t shy away from fully fleshing-out proofs and repeating relatively similar cases with some additional notes e.
The book itself can certainl Overall, great introductory book to topology. I struggled quite a bit with the intuition behind some of the proofs, and have, more than once, rolled around on my bed trying to recall or prove again some particular statement that I found quite useful. Sadly, the book doesn’t have a section on homotopy equivalence and some other useful notions, but do recall it is an introduction in exactly pages menddlson short text. This book took me at least hours topoolgy get through, skipping only the very latter section of the compactess chapter and doing at least two of the harder problems in each section; but I have very little experience with analysis, something I’m sure would have helped complete this and gain the corresponding intuition much more quickly.
Again, great book which I would highly recommend for self-study. Apr 19, Dean Allison rated it liked it. I have the patience of a hummingbird.
An Introduction to Topology is a consistent, accessible, and charming compendium of a few higher branches of symbolic maneuvering. I dare you to read it. Jun 24, David inhroduction it really liked it. Excellent resource for learning about topology, although I wasn’t really prepared for several proofs and exercises so it was hard to wrap my mind around some concepts. Overall a good book. Aug 13, Abdullah Najjar rated it did not like it. I was expecting something more readable.
This book seems very difficult for an introduction. Therefore, I am going to buy another books about this subject and then compare introductiion with this one. Jun 02, Eyad Berh rated it really liked it. Menndelson 25, Kiehl Christie rated it liked it. Mar 18, Eric Regina rated it really liked it Shelves: Good, but very quick and straight to the point. You will find maybe a paragraph or two of intuition.