Unformatted text preview: Q . Show there is one and only one way of extending it to the reals as a continuous function ˜ f : R → R . (6) Show that a Cauchy sequence is bounded (as a set). Conclude that unbounded sequences cannot converge. (7) Find an example of a bounded set B and a continuous function f : R → R such that f ( B ) is not bounded. (8) Show that R is not compact. (9) Show that a bounded set in R is totally bounded. 1...
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 Spring '09
 DANBERWICK
 Math, Topology, Division, Continuous function, Cauchy sequence, Xn

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