Abstract
A typical (in the sense of Baire category) compactA inE, whereE is either the Euclidean spaceE 8,s≧2, or the separable Hilbert space ℍ, generates a dense subsetC n,m(A) of the underlying space, such that everyx∈C n,m(A) has exactlyn nearest andm farthest points fromA, whenevern andm are positive integers satisfyingn+m≦ dimE+2.
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