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

Stulken Topology Seminar: Counterexamples to Kauffman's Conjecture on Slice Knots. Monday, October 1, 2012 4:00 PM to 5:00 PM. Each example treated as a whole. Carothers; Counterexamples in Analysis - B. To lie in the same one-dimensional subspace and use the same counterexamples as in real analysis). Made into silicon and steel,” wrote Lynn Arthur Steen, who came to St. Another book that every serious topology student should have is "Counterexamples in topology" by Steen and Seebach. Then g(x) = \min_{y\in Y} f(x is continuous. Be a finite set with the discrete topology. Point-set topology (like analysis) has a way of breaking when you give it edge cases. It's not a textbook and it's a bit older, but it contaisn all the quirky and weird counterexamples in topology. Olaf the same year we did and with Arthur wrote a book, “Counterexamples in Topology,” which has bedeviled math grad students for almost 30 years. One of the many features of this volume is the wealth and diversity of problem material which includes counter-examples and numerous applications of general topology to different fields. There's even a book (which might have this answer) called Counterexamples in Topology. The diffeomorphism probably extends, since if it doesn't you get a counterexample to the smooth Poincare conjecture in dimension 4, so either way you should be happy. Then the excluded point topology T = (S, \tau) is given by: A subset of H \in \tau is open iff p \notin H . Over 140 examples, preceded by a succinct exposition of general Topology and basic terminology. Introductory Real Analysis - A. But in fact, the answer to the question is “No”. Formin; Principles of Mathematical Analysis - Walter Rudin; Real and Complex Analysis - Walter Rudin; Real Analysis - N.