APPROXIMATION OF COMPACTA IN<i>Eⁿ</i>IN CODIMENSION GREATER THAN TWO

Abstract

The following is proved. Theorem. For a compactum of codimension greater than or equal to three lying in Euclidean space there exists an arbitrarily close approximation by a locally homotopically unknotted (1-ULC) imbedding. A series of corollaries about approximation of imbeddings of manifolds and polyhedra is derived. A problem about Menger universal compacta is solved. The article contains the complete proof of previously announced results stated in the references. Bibliography: 17 items.