Unformatted text preview: C such that their intersection is not connected. 4. Show that the set C \{ z  z ∈ R and z ≤ } (that is the set of complex numbers without negative real numbers) is open and connected. 5. Find the limit of each sequence that converges; if the sequence diverges, explain why. a) z n = ± 1 + i √ 2 ² n , b) z n = Arg ((1 + ni ) 2 ) , c) z n = n 2 ± i 2 ² n 6. Let A be a closed set and lim n →∞ z n = w . Show that if z n ∈ A for all n then w ∈ A . 7. Show that the statement of the previous problem would not be true in general if A was an open set. In other words present an open set A and a convergent sequence, such that all the elements of the sequence are in A but the limit is not in A ....
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 Spring '09
 Topology, Metric space, Topological space, Closed set, General topology

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