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Finiteness of Sets

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Give examples to show that the finiteness of the collections in parts c and d is essential.

c) for any finite collection G1, G2, ...., Gn of open sets, intersection (at the top of the intersection sign is n and at the bottom is i=1) of Gi is open.

d) For any finite collection F1, F2, ...., Fn of closed sets, union sign (with n at the top of the sign and i=1 at the bottom) of Fi is closed.

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For the following problems, we all consider metric ...

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Finiteness of sets is investigated. The solution is detailed and well presented.

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