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Unformatted text preview: You can assume that this gives a well-dened topology. (a) Show that the standard topology on R 2 n = C n is ner than the Zariski topology. ( Note: By ner, I always mean at least as ne; see the Denition in Munkres, p. 77.) (b) Consider the subset A C n consisting of all points of the type ( s, , . . . , 0) with s Z . Prove that A is not closed in the Zariski topology. Conclude that the standard topology is strictly ner than the Zariski topology. Challenge (extra credit): Munkres, Ch.2 17, exercise 21 on p. 102....
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- Spring '05