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...
View
Full Document
 Spring '11
 sdd
 Math, Topology, Metric space, Topological space, Closed set, compact Hausdorff space, limit topology Rl

Click to edit the document details