 Thus "f"("e""n") meets at most finitely many cells of "Y", so we can take formula_2 to be a cell of highest dimension meeting "f"("e""n").If formula_3, the map "f" is already cellular on "e""n", since in this case only cells of the "n"-skeleton of "Y" meets "f"("e""n"), so we may assume that "k" > "n".It is then a technical, non-trivial result (see Hatcher) that the restriction of "f" to formula_4 can be homotoped relative to "X""n-1" to a map missing a point "p" ∈ "e""k".