Geodesic
Embedding compacta in Euclidean space of dimension~$5$, $4$ and~$3$
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 563-569

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In this paper results concerning the notion of dimension of an embedding, earlier obtained for embeddings of compacta in Euclidean space $E_n$ for $n\geqslant6$, are extended to the case $n=5$. For $n=4$ a reduction of the main problem to the so-called open four-dimensional Poincaré conjecture is given, and some sufficient conditions are given for $n=3$. Bibliography: 14 titles. 
@article{SM_1976_28_4_a8,
     author = {M. A. Shtan'ko},
     title = {Embedding compacta in {Euclidean} space of dimension~$5$, $4$ and~$3$},
     journal = {Sbornik. Mathematics},
     pages = {563--569},
     publisher = {mathdoc},
     volume = {28},
     number = {4},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_4_a8/}
}
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M. A. Shtan'ko. Embedding compacta in Euclidean space of dimension~$5$, $4$ and~$3$. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 563-569. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a8/