Vol. 51, No. 1, 1974

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Sets which are tame in arcs in E3

Richard Detmer

Vol. 51 (1974), No. 1, 67–74

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.

Mathematical Subject Classification
Primary: 57A10
Secondary: 57A30
Received: 12 December 1972
Published: 1 March 1974
Richard Detmer