Geodesic
Imbedding of locally unknotted one-dimensional manifolds in~$E^3$
Sbornik. Mathematics, Tome 10 (1970) no. 2, pp. 267-287

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It is shown that each locally unknotted simple arc in three-dimensional euclidean space $E^3$ lies on a disc $D\subset E^3$, whence it follows that there exists a pseudo-isotopy of the space $E^3$ which carries a line segment into the locally unknotted simple arc. Bibliography: 16 titles. 
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     author = {Lyudmila Keldysh},
     title = {Imbedding of locally unknotted one-dimensional manifolds in~$E^3$},
     journal = {Sbornik. Mathematics},
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     volume = {10},
     number = {2},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_10_2_a7/}
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Lyudmila Keldysh. Imbedding of locally unknotted one-dimensional manifolds in~$E^3$. Sbornik. Mathematics, Tome 10 (1970) no. 2, pp. 267-287. http://geodesic.mathdoc.fr/item/SM_1970_10_2_a7/