EMBEDDING COMPACTA IN EUCLIDEAN SPACE OF DIMENSION 5, 4 AND 3

In this paper results concerning the notion of dimension of an embedding, earlier obtained for embeddings of compacta in Euclidean space En for n≥6, are extended to the case n=5. For n=4 a reduction of the main problem to the so-called open four-dimensional Poincare conjecture is given, and some sufficient conditions are given for n=3. Bibliography: 14 titles.