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

Over 140 examples, preceded by a succinct exposition of general Topology and basic terminology. A counterexample is given by the topology of finite complements. ASIN 048668735X Counterexamples in Topology (Dover Books on Mathematics) - ASIN:048668735X - AS 5ee014dae477d65a6aaa48e43b39a316. Yes, sequentially compactness has nothing to do with compactness in general topological spaces. A naive approach to the problem of constructing “convenient categories” usually runs into problems. Does it mean a morphism which is a surjection of sheaves in the fpqc topology? A brief foray through Amazon.com revealed catalogues of well known counter examples in topology, analysis, and graph theory. Counterexamples in Topology (Dover . It's not a textbook and it's a bit older, but it contaisn all the quirky and weird counterexamples in topology. The Hawaiian earring space is a famous counterexample in topology which shows the need for care in hypotheses to develop a good theory of covering spaces. Another book that every serious topology student should have is "Counterexamples in topology" by Steen and Seebach. Every compact topological manifold can be triangulated by a locally finite simplicial complex. In that case you get counter examples by looking at ind schemes (for example the functor of morphisms A^1 —> A^1). 2, Vector and Tensor Analysis; . Each example treated as a whole. The Geometric Topology of 3-Manifolds (Colloquium Publications) [R.