TITLE: Looking for challenge problems in topology
QUESTION [5 upvotes]: Right now my friend and I are going through Munkres Topology and we meet up to work on the challenge problems. I am wondering if anyone knows of a good resource or if someone could post some difficult questions. Right now we are mostly focusing on stuff before the quotient topology in Munkres.
Any help much appreciated.

REPLY [5 votes]: Read through the classic Counterexamples in Topology and fill in the relevant details as you go along. Many interesting examples of spaces are given, but often without the detailed proofs that they have the properties that the book claims that they have (since that would bloat the book and make it less useful as a reference).