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

Counterexamples are easy to find. Vols.1-2.(Dover, 1992)(669s).pdf 14.19 MB Complex Variables - Introduction and Applications 2nd ed - M. Is this true for the box topology? So Tychonoff theorem states products of compact sets are compact in the product topology. Some counterexamples in topology. Algebraic Topology an Intuitive Approach - H. Another book that every serious topology student should have is "Counterexamples in topology" by Steen and Seebach. It's not a textbook and it's a bit older, but it contaisn all the quirky and weird counterexamples in topology. Venkatamarana; Counterexamples In Topology - Steen , Seebach; Curvature and . (Fortunately the term topological groupoid is not taken by this tradition; indeed, the only groupoid that is a topological category over Set is trivial. Mathematics > Functional Analysis Simple counterexamples show that the discussed phenomenon does not hold in general, but it is established in a wide class of cases. Product of compact sets compact in box 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. I am looking for a non-continuous function f:X-->Y where X,Y are non-countable spaces, but where lim n-->∞ xn = x.