Does every homeomorphism of the unit sphere S^n, n=2, has diffeomorphic extension to the unit ball. I am indeed interesten about the reference of the following problem: I need a given homeomorphism $h$ of the unit sphere to approximate uniformly by a sequence of diffeomorphisms $h_i$.
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Dear Igor Rivin, indeed I possed two questions: a) Does every homeomorphism of the unit sphere S^n, has diffeomorphic extension to the unit ball which is a homeomorphism in the closed unit ball. b) For a given homeomorphism h of the unit sphere S^2 onto itself, does there exists sequence of diffeomorphisms h_i of the unit sphere onto itself that converges uniformly to h. My first impression was that a) implies b), but I am not sure in that. I think both answers are YES but I need a reference (in particular I am interested in question b) 

