Geodesic
Approximation of imbeddings of manifolds in codimension one
Sbornik. Mathematics, Tome 23 (1974) no. 3, pp. 456-466
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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 Chernavskii 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 titles. 
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M. A. Shtan'ko. Approximation of imbeddings of manifolds in codimension one. Sbornik. Mathematics, Tome 23 (1974) no. 3, pp. 456-466. http://geodesic.mathdoc.fr/item/SM_1974_23_3_a8/

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