A surface is tame if its complement is 1-ULC
R. H. Bing · Transactions of the American Mathematical Society · 1961
Introduction. In this paper we show that a 2-manifold M in Euclidean 3-space E3 is tame if E3 -M is uniformly locally simply connected.A closed subset X of a triangulated manifold Y is tame if there is a homeomorphism of Y onto itself taking X onto a polyhedron (geometric complex) in Y.If there is no such homeomorphism, X is called wild.Examples of 2-