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Unformatted text preview: intersection of countably many open sets. (Hint: problem 2. part (e) above.) (c) Show that every open set in a metric space can be expressed as an union of countably many closed sets. (Hint: take complements.) (d) Express the interval (0 ; 1) in R as a union of countably many open sets. 4. Let ( M;d ) be any metric space and let A be a &nite set in M: (a) Show that A is closed and bounded. (b) Without using any theorems, just using the de&nition show that A is sequentially compact. (c) Without using any theorems, just using the de&nition show that A is totally bounded. 1...
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 Fall '08
 ALBERTERKIP
 Math, Sets

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