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Counterexamples in Topology Lynn Arthur Steen, J. Arthur Seebach
Publisher: Dover Publications

Topology Notes (FREE!) Thurston W.P. Wikipedia has a [.gif] to demonstrate this. Someone I know has a database of topological spaces, mostly extracted from the book "Counterexamples in Topology". There's even a book (which might have this answer) called Counterexamples in Topology. Introductory Topology: Topology is an extension of geometry and built on set theory, it's about continuity. Point-set topology (like analysis) has a way of breaking when you give it edge cases. Counterexamples in Topology; Strickland N. Lecture Notes on Elementary Topology and Geometry; Steen L.A. You may have studied Singer I.M. There is a joke that topologists are those who cannot distinguish between a doughnut and a coffee or tea cup. I like this comment very much; and I like the idea of developing better tools to prove the existence of counterexamples. A naive approach to the problem of constructing “convenient categories” usually runs into problems.