This article is cited in 1 paper

Imbedding of locally unknotted one-dimensional manifolds in $E^3$

Lyudmila Keldysh


Abstract: 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.

UDC: 513.83

MSC: 53A04, 58D10, 57N12

Received: 26.06.1969

 English version: Mathematics of the USSR-Sbornik, 1970, 10:2, 267–287

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