Let B denote the closed unit ball in a finite-dimensional normed linear space
B = {x ∊ X: ||x|| ≤ 1}
and let S denote its boundary, that is,
S = {x ∊ X: ||x|| ≤ 1}
There is no continuous function r: B → S such that r(x) = x for every x ∊ S.