Where can I find challenging topology questions I was hoping someone might be able to refer me to a collection of hard(er) general topology questions at undergraduate level. Many thanks!
 A: Considering that you're asking for harder problems, I disagree with the suggestion of Munkres. Sorry for being blunt, but that book is really targeted at people with a low level of mathematical maturity.
I won't suggest reference books on topology like Dugundji, Engelking or Bourbaki either, because the problems will be divided among the chapters and often connected with specialized advanced material in each chapter.
Instead, I'd suggest either the topology chapters in books on analysis or introductory books on topology written at a higher level than Munkres. Here are some examples.

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*General Topology by Willard. (In this case, the problem with specialized material occurs to some extent.)

*Topology by Choquet.

*The topology chapters of Real and Functional Analysis by Lang. (Don't forget to look at the parts on normed vector spaces in this book or any other. Even basic material on Euclidean space is to be found there.)

*Volume 2 of Mathematical Analysis by Zorich (Chapter 9 and Sections 10.1, 10.2).

*Treatise on Analysis by Dieudonné. Chapters III-VII (in Volume 1, on metric spaces, the real line, normed vector spaces, Hilbert spaces, and spaces of functions) and Chapter XII (in Volume 2, on general topology).

A: Topology by Munkres (inventive name as with most math books) has many good exercises, some of which are very challenging. The undergraduate topology course I took used this book and I feel that it gave me a solid background in topology, and I remember it well over a decade later despite not ending up specializing in it.
