On the Extension of Analytic Sets into a Neighborhood of the Edge of a Wedge in Nongeneral Position

Let $K = D_+\cup T^n\cup D_-$ be an $n$-circled two-sided wedge in $\mathbb C^n$ where the unit polycircle (torus) $T^n$ plays a role of the edge, and domains $D_{\pm}$ adjoined to $T^n$ may not contain any full-dimensional cone near $T^n$. In this case we say that the wedge $K$ is in nongeneral position. Consider a question when the closures of pure $n$-dimensional analytic sets $A_{\pm}\subset D_{\pm}\times\mathbb C^m$ compose a single analytic set in a neighborhood of the wedge $K\times\mathbb C^m$. If $K$ is in general position then the answer to the question is given by the theorem of S. I. Pinchuk. In the present article we expand this theorem to the case when the two-circled wedge $K$ is in nongeneral position, and $m = 1$.