I know many people who learned point set from Armstrong rather than Munkres.
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I have personally only cursorily glanced through Armstrong, and I found it roughly comparable to Munkres. When I read the reviews on Amazon for Munkres and Armstrong , however, there is a strange discrepancy. Munkres far outscores Armstrong whatever that really means. Perhaps this is due to the recurring theme in the top reviews of Armstrong, which say that Armstrong deviates from the logical and some would say, intuition-less flow of Munkres to instead ground the subject in a diverse set of subjects.
On the other hand, this review says that Munkres is simply more extensive. On a different note, there is a freely read but not printed book by S. Morris called Topology without tears. This is a link to the pdf on his website.
I should note that the version linked is not printable. I think this book is very readable, and is perhaps the gentlest introduction text here for better or worse.
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It comes very highly recommended for those interested in that niche. But the homology theory section is… lacking. Finally, John Stillwell wrote a book Classical Topology and Combinatorial Group Theory which has a very interesting presentation and selection of material is atypical. But it seems like a pretty interesting angle of approach. It actually introduces point-set, algebraic, and differential topology as well as some differential geometry.
So it is absolutely not a replacement for learning point-set topology. Counterexamples might be particularly nice, because Munkres has a tendency to give really pathological counterexamples sometimes. This includes:. I learned from this book, and my initial dislike I had a hard time with some of the initial arguments turned into a sort of respect. But it has a very nice bibliography for further reading.
Tammo Tom Dieck has a new book, Algebraic Topology , which just might be loved even by Hatcher himself.
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There are also some additional free sources of notes. There are complete lecture notes of K. Wurthmuller and Gregory Naber available at their websites and elsewhere. In terms of general topology, unusual features are the motivation for the open set axioms for a topology; a categorical approach, using universal properties in a clear way, thus giving an emphasis on constructing continuous functions; a geometric approach, using adjunction spaces; a gluing theorem for homotopy equivalences; and much else.
Ross Geoghegan in his review MR of two papers by M. Personalize Gift card We will send an email to receiver for gift card.
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