... 8π2 and k ≥ 1 the same is true with Ak,kreplaced bySk−1.We divide the section into two parts. First we derive some properties of the set Mkfor k ≥ 1. Then we turn to the construction of the ... combinations of the formli=1αixi,αi≥ 0,iαi= 1. To do this, we consider the embedding of M into someRngiven by Whitney’s theorem, take the convex combination of the images of the points ... s (and nonzero), and therefore on this set Ψ ◦ ΦS,λcan beeasily contracted to the boundary of Bk1(recall the definition of Ak,k), as for the identity map. This concludes the proof in the...