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Apr 6, 2010 at 4:20 comment added gondolier I think what is lacking here is convexity. Otherwise, one can make use of this selection theorem: en.wikipedia.org/wiki/Michael_selection_theorem
Apr 6, 2010 at 3:56 comment added gondolier alright. I think this is impossible in general. Example: $n = 2, k =1$. $S = [-1,0] \times $ {1} $\cup$ $[0,1] \times $ {0}. Then T=[-1, 1] . There is a problem at y=0
Apr 6, 2010 at 3:02 history asked gondolier CC BY-SA 2.5