Geodesic
Imbedding of zero-dimensional compacta in~$E^3$
Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 99-114

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In this paper, for an arbitrary zero-dimensional compactum $P$ in $E^3$, a pseudoisotopy $F_t$ of the space $E^3$ onto itself is constructed, taking a tame zero-dimensional compactum $C$ into $P$; here each nondegenerate preimage of a point under the mapping $F_1$ is a tame arc. For the zero-dimensional Antoine compactum $A$ a pseudoisotopy $F_t$ of $E^3$ onto itself is constructed taking a tame zero-dimensional compactum into it so that the mapping $F_1$ has a countable set of nondegenerate primages of points, but each of these is not a locally connected continuum. Bibliography: 11 titles. 
@article{SM_1971_14_1_a5,
     author = {E. V. Sandrakova},
     title = {Imbedding of zero-dimensional compacta in~$E^3$},
     journal = {Sbornik. Mathematics},
     pages = {99--114},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_1_a5/}
}
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E. V. Sandrakova. Imbedding of zero-dimensional compacta in~$E^3$. Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 99-114. http://geodesic.mathdoc.fr/item/SM_1971_14_1_a5/