Abstract
Let
X
be a topological space,
U
-- opened subset of
X
. We will say that point
x∈∂U
is {\it accessible} from
U
if there exists continuous injective mapping $\phi : I \to \Cl D$ such that
ϕ(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
∖D
are connected; 2) any
x∈∂D
is accessible both from $\Int D$ and from
R
2
∖D
.