Geodesic
$k$-Regular maps into Euclidean spaces and the~Borsuk--Boltyanskii problem
Sbornik. Mathematics, Tome 193 (2002) no. 1, pp. 73-82

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The Borsuk–Boltyanskii problem is solved for odd $k$, that is, the minimum dimension of a Euclidean space is determined into which any $n$-dimensional polyhedron (compactum) can be $k$-regularly embedded. A new lower bound is obtained for even $k$. 
@article{SM_2002_193_1_a1,
     author = {S. A. Bogatyi},
     title = {$k${-Regular} maps into {Euclidean} spaces and {the~Borsuk--Boltyanskii} problem},
     journal = {Sbornik. Mathematics},
     pages = {73--82},
     publisher = {mathdoc},
     volume = {193},
     number = {1},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_1_a1/}
}
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S. A. Bogatyi. $k$-Regular maps into Euclidean spaces and the~Borsuk--Boltyanskii problem. Sbornik. Mathematics, Tome 193 (2002) no. 1, pp. 73-82. http://geodesic.mathdoc.fr/item/SM_2002_193_1_a1/