APPROXIMATION OF IMBEDDINGS OF MANIFOLDS IN CODIMENSION ONE
M A Štan'ko · Mathematics of the USSR-Sbornik · 1974
It is shown that any (n - 1)-manifold topologically imbedded in a euclidean space of dimension greater than four can be approximated arbitrarily closely by one whose complement has the property of uniform local one-connectedness. From this theorem and the results of Cernavskiĭ and Kirby-Siebenmann it is deduced that there also exists a piecewise linear approximation if the dimension of the euclidean space is greater than five. Bibliography: 15 items.