Unformatted text preview: a, b ). (7) Show that ( a, b ] is incomplete and that [ a, b ] is complete. (8) Show that if x is a limit point of the set A then there is a sequence { x n } ∞ n =0 in A which converges to x . (Hint: take ±balls around x , with radii decreasing to 0.) (9) Show that the closed ball, B ± ( a ) := { x  d ( x, a ) ≤ ± } is a closed set. (10) Find an example where the inﬁnite intersection of open sets is not open and one where the inﬁnite union of closed sets is not closed. 1 Comic from www.xkcd.com 1...
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 Spring '09
 DANBERWICK
 Topology, Division, Sets, Metric space, Topological space, closed sets

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