Results of McMillan and
Cannon may be combined to give an algebraic condition which is sufficient to show
that an arc topologically embedded in E3 is tame in E3. The main theorem of this
paper gives an essentially algebraic condition involving an arc embedded in E3 and a
compact subset of that arc which is sufficient to show that the arc may be
approximated arbitrarily closely without moving the subset, to obtain a tame
arc.