Abstract
In domain Ω ⊂ En it is considered a set of smooth lines such that through a point X ∈ Ω passed one line of given set. The moving frame is frame of Frenet for the line ωi of the given set. Integral lines of the vector fields are formed net ∑n of Frenet. There is exist the point on the tangent of the line ωi. When the point X is shifted in the domain Ω, the point describes it’s domain in En. It is defined the partial mapping such that Necessary and sufficient conditions of of quasi-double lines of the partial mapping of space En are proved.
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