Charles Pugh, Michael Shub, et al.
Duke Mathematical Journal
Paper
Critical sets in 3-space
Abstract
Given a non-empty compact set C ⊂R 3, is C the set of critical points for some smooth proper function f 3 →R +? In this paper we prove that the answer is "yes" for Antoine's Necklace and most but not all tame links. © 1993 Publications Mathématiques de L'I.É.E.S.
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