J. Dugundji, “Topology,” Allyn and Bacon, Inc., Boston, has been cited by the following article: TITLE: Continuous Maps on Digital Simple Closed Curves. James Dugundji (August 30, – January, ) was an American mathematician, Dugundji is the author of the textbook Topology (Allyn and Bacon, ), Dugundji, J. (), “An extension of Tietze’s theorem”, Pacific Journal of. J. Dugundji. Topology. (Reprint of the Edition. Allyn and Bacon Series in try/topology sequence, and accordingly no detailed knowledge of definitions.
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As an introductory book, ” Topology without tears ” by S. You can download PDF for free, but you might need to obtain a key to read the file from the author.
He wants to make sure it will be used for self-studying. The version of the book at the link given above is not printable. Here is the link to the printable version but you will need to get the password from the author by following the instructions he has provided here.
Munkres said when he started writing his Topology, there wasn’t anything accessible on undergrad level, and both Kelley and Dugunji wasn’t really undergrad books. He wanted to write something any undergrad student with an appropriate background like the first chapters of Rudin’s Principles of Analysis can read.
He also wanted to focus on Topological spaces and deal with metric spaces mostly from the perspective “whether topological space is metrizable”. That’s the dugudji half of the book. The second part is a nice introduction to Algebraic Topology. Again, quoting Munkres, at the time he was writing the book he knew very little of Algebraic Topology, his speciality was General point-set topology.
So, he was topologyy that second half as he was learning some basics of algebraic topology. So, as he said, “think of this second half as an attempt by someone with general topology background, topolog explore the Algebraic Topology. Perhaps you can take a look at Allen Hatcher’s webpage for more books on introductory topology. A slim book that gives an intro to point-set, algebraic and differential topology and differential geometry.
It does not have any exercises and is very tersely written, so it is not a substitute for a standard text like Munkres, but as a beginner I liked this book because it gave me the big picture in one place without many prerequisites. Seebach and Steen’s book Counterexamples in Topology is not a book you should try to learn topology from.
But as a supplemental book, it is a lot of fun, and very useful. Munkres says in introduction of his book that he does not want to get bogged down in a lot of weird counterexamples, and indeed you don’t want to get bogged down in them.
But a lot of topology is about weird counterexamples. What is the difference between connected and path-connected?
Dugundji J., Topology | Luis Alberto –
What is the difference between compact, paracompact, and pseudocompact? Browsing through Counterexamples in Topology will be enlightening, especially if you are using Munkres, who tries hard to avoid weird counterexamples. This answer dugujdji also posted hereon a question which is now closed. You might consider Topology Now! Their idea is to introduce the intuitive ideas of continuity, convergence, and connectedness so that students can quickly delve into knot theory, the topology of surfaces and three dimensional manifolds, fixed points, and elementary homotopy theory.
I wish this book had been around when I was a student! I own Bert Mendelson’s ” Introduction to Topology ” and it looks good. I bought Alexandroff’s ” Elementary Concepts of Topology ” too – believe me, it’s not good for an introduction. You might look dugunsji the answers to this previous MSE question, which had a slightly different slant: Apparently the poster was also interested in self-learning, but with less preparation than you.
Furthemore, the book is brilliantly written and covers almost everything. One of the best books of the Bourbaki series. I know a lot of people like Munkres, but I’ve never been one of them.
When I read sections on Munkres about things I’ve known for years, the explanations still seem turgid and overcomplicated.
I like John Kelley’s book General Topology a lot. I find the writing stunningly clear. It has been in print for sixty years. You should at least take a look at it. I recommended Viro’s Elementary Topology. This book is very well structured and has a lot of exercises, the only thing is it do not talk about uniform topoloy, I think for this part topoloyg can read Kelley or Bourbaki.
There was another version of this question posted today, and it inspired me to write another MSE-themed blog post. So I have tolology most of the topology recommendations from MSE and a few from MO and a few other sources and written up a post at my blog, mixedmath. Hope I didn’t miss this above: But don’t think of it as nepotism the authors and T.
Tao said in the syllabus that the text will be followed closely. Actually the book is replete with examples as each section is followed by questions which are answered at the back of the book.
And a special consideration – it is as a noted mathematician coined the term Doverised. See this mathoverflow discussion. Wilansky has an excellent section on Baire spaces and induced topologies. It’s a little wordier than Gaal, but has many topologj exercises.
Laures duguncji Szymik write an excellent book on topology that incorporates category theory seamlessly. The proofs are also very different from the typical presentations I see in American books. It’s good for a second pass through tipology topologythat is, if you read German.
Best book for topology? I’m not sure if there’s such a thing as “the” best general, I’m assuming topology textbook. I learned the basics from the first general half of Munkres, which I liked. I found that later, when I took abstract real analysis, I really liked the concise but still relatively comprehensive treatment in Folland’s text on real analysis Chapter 4.
Of course it’s not Bourbaki’s General Topology or anything, in terms of coverage, but I still really like it. Incidentally, I also like Bourbaki’s General Topology at least the first volume, which I’m more familiar with.
Do you know what kind of “topology” you want to learn? Topology is a wide subject-area and there are many entry-points.
James Dugundji – Wikipedia
Other than point-set topology which most of the comments below are addressingdifferential topology is also a nice entry-point. Texts by Guillemin and Topllogy, Milnor and Hirsch with that or similar titles are all very nice. Another standard entry-point might be a knot theory textbook. Like say Adams’s book “The knot book” or something similar.
I am now only looking for good books. Also, another great introductory book is Munkres, Topology. On graduate level non-introductory books are Kelley and Dugunji or Dugundji? For what it’s worth, Munkres’s algebraic topology only goes into the fundamental group and the theory of covering spaces. If you’re interested dughndji the subject, I recommend Allen Hatcher’s book, which is available for free on his webpage.
Munkres is great k point-set, but not so good for algebraic. Sorry to revive this. But where did you get those comments by Munkres?
Matematik 3GT Fall 2004
Dugundhi CAN read it, but I am spending so much time on each page that I came here looking for a book with more words in these poofs. Definitely gives an otherworldly perspective though.
I would suggest the following options: Armstrong Perhaps you can take a look at Allen Hatcher’s webpage for more books on introductory topology.
A note about Munkres: For me, there was very little in the way of intuition in using that book. Also, many counterexamples were quite pathological when simpler counterexamples sufficed. I’ll that in mind.
I will second the suggestion for Munkres. It is the book I used in my undergraduate topology class, and contains both trivial and non-trivial examples Bey, I find some of the more obscure counterexamples to be more interesting in the end, as they provide a perspective I may have not seen myself. You will ultimately want a more advanced book as Keenan mentioned abovebut for the basics Munkres is a great book. I think the way one builds intuition using Munkres is by doing lots of exercises at least that worked for me when I took his class rather than having it spoonfed to you.
And the pathological nature of the counterexamples is part of the intuition one builds, in the sense dugundj it tells you just how bad the situation can be. I’ll try to see this one!
Scott Feb 13 ’12 at I also like Bourbaki’s treatise, but some times it is a bit too logical. Scott Maybe not I borrowed it to someone and forgot it – so I miss it anyway vugundji. Feb 14 ’12 at 6: BTW Kelly is a bit oldish in style – which I don’t really like. I consider at most the first of those important for an introductory text in point-set topology.