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This question tries to highlight that the intersection of an infinite number of open sets may or may not be open. Similarly, the union of
This question tries to highlight that the intersection of an infinite number of open sets may or may not be open. Similarly, the union of an infinite number of closed sets may or may not be closed.
(a) If Sn = (n, n + 1), then prove that T nN++ Sn is both open and closed.
(b) If Sn = ( 1 n , 1), then prove that T nN++ Sn is neither open and nor closed.
(c) If Sn = [n, n], then prove that S nN++ Sn is both open and closed.
(d) If Sn = [ 1 n+1 , 1 1 n+1 ], then prove that S nN++ Sn is open and not closed.
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