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

Product of compact sets compact in box topology? The particular point topology is defined in the following way: given some space X , we let p\in X be a distinguished (or particular) point. Counterexamples in Topology Lynn Arthur Steen, J. Download Counterexamples in Topology. It's not a textbook and it's a bit older, but it contaisn all the quirky and weird counterexamples in topology. Is this true for the box topology? I just used this counter-example, so I felt like I should share it with all of you guys. So Tychonoff theorem states products of compact sets are compact in the product topology. The definitions of the separation axioms I used to make these are taken from Counterexamples In Topology. Another book that every serious topology student should have is "Counterexamples in topology" by Steen and Seebach.