Abstract
A wild Cantor set in S 3 is constructed with simply connected complement. It is proved that a Cantor set C ⊂ S 3 is tame if and only if every piecewise-linear, unknotted, simple loop in S 3⧹ C may be engulfed. And a Cantor set C ⊂ S 3 is tame if and only if π 1( S 3⧹ C ⧹ K) is finitely generated for all piecewise-linear, unknotted, simple loops K in S 3⧹ C .
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