Abstract
A 2-sphere S in Euclidean 3-space E 3 {E^3} is defined to be homogeneous over the subset X of S if for each p, q ∈ X q \in X there is a homeomorphism h : E 3 → E 3 h:{E^3} \to {E^3} such that h ( S ) = S h(S) = S and h ( p ) = q h(p) = q . It is shown that a 2-sphere S in E 3 {E^3} is tame from one side provided S is locally tame modulo a tame 0-dimensional set C such that S is homogeneous over C. An example is described to show that it is necessary to require that C be tame.
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