In this paper it is shown that there exist open connected subsets
D
1
,
D
2
{D_1},{D_2}
, and
D
3
{D_3}
of an
n
n
-cell
E
E
such that, if
C
C
is any proper compact connected subset of
E
E
and
C
⊂
U
,
U
C \subset U,U
open, then there exists a homeomorphism
h
h
of
E
E
onto itself such that
C
⊂
h
(
D
i
)
⊂
U
C \subset h({D_i}) \subset U
for some
i
,
1
≦
i
≦
3
i,1 \leqq i \leqq 3
.