Wild Cantor sets as approximations to codimension two manifolds (Q578661)

The authors establish a technique for constructing wildly embedded Cantor sets in Euclidean n-space \(E^ n\). For any compact (n-2)-manifold M embedded in \(E^ n\) \((n>2)\) with a closed neighborhood W homeomorphic with the product of M and a 2-cell, it gives a Cantor set C in W such that a loop in the complement of W is contractible in the complement of C if and only if it is contractible in the complement of M. The result generalizes a construction of \textit{L. Antoine} [J. Math. Pures Appl., VIII. Sér. 4, 221-325 (1921)] and is much more useful than a previous generalization due to \textit{W. A. Blankinship} [Ann. Math., II. Ser. 53, 276-297 (1951; Zbl 0042.176)]. The authors first announced their construction in 1974. Since that time, their work has been referred to by several authors. This paper fills an important gap in the mathematical literature.