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Unformatted text preview: A be a subset of X . Deﬁne d ( x,A ) = glb { d ( x,a ) : x ∈ A } . a. Show that f : X → R , deﬁned by f ( x ) = d ( x,A ), is continuous function. b. Is it true that for some a ∈ A , we have d ( x,A ) = d ( x,a )? Is this true if A is closed? If A is compact? Problem 6. Show that the set [0 , 1] is not limit point compact as a subspace of R l . Problem 7. Let X be limit point compact. If A is a closed subset of X , is A necessarily limit point compact? 1...
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 Spring '11
 sdd
 Math, Topology

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