Unformatted text preview: A is a collection of sets B satisfying: (a) Each B ∈ B is open. (b) A is contained in the union of sets in B , i.e. A ⊆ [ B ∈B B . Show that B = ±² 1 n , n1 n ³ for n = 0 , 1 , 2 ,... ´ is an open cover of (0 , 1). Is there a ﬁnite subset of B that is an open cover of (0 , 1)? 6. Prove that when A and B are countable, A × B is countable. 7. Let f : A → B and C,D ⊆ B . Prove f1 ( C ∪ D ) = f1 ( C ) ∪ f1 ( D ). What about f1 ( C ∩ D )? 1...
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 Winter '11
 Wiley
 Differential Equations, Equations

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