On the imbedding of a finite family of closed disks into a plane or S^{2}

Let $\{V_i{\}}_{i=1}^n$ be a finite family of closed subsets of a plane or a sphere $S^2$, each homeomorphic to the two-dimensional disk. In this paper we discuss the question how the boundary of connected components of a complement ${\text{rr}}^2\setminus {\bigcup }_{i=1}^n{V}_i$ (accordingly, $S^{2} \setminus \bigcup_{i=1}^{n} V_{i}$) is arranged. It appears, if a set ${\bigcup }_{i=1}^n\text{Int}{V}_i$ is connected, that the boundary $\mathrm{\partial }W$ of every connected component $W$ of the set $\rr^{2} \setminus \bigcup_{i=1}^{n} V_{i}$(accordingly,$S^{2} \setminus \bigcup_{i=1}^{n} V_{i}$) is homeomorphic to a circle.