  Let $X$ be a topological space, $U$ -- opened subset of $X$. We will say that
point $x \in \partial U$ is {\it accessible} from $U$ if there exists
continuous injective mapping $\phi : I \to \Cl D$ such that $\phi(1)=x$,
$\phi([0,1)) \subset \Int U$.
  We proove the next main theorem. The following conditions are neccesary and
suffficient for a compact subset $D$ of $R^2$ with a nonempty interior $\Int D$
to be homeomorphic to a closed 2-dimensional disk: 1) sets $\Int D$ and $R^2
\setminus D$ are connected; 2) any $x \in \partial D$ is accessible both from
$\Int D$ and from $R^2 \setminus D$.
