Let
X
X
be a homogeneous continuum and let
E
n
{E^n}
be Euclidean
n
n
-space. We prove that if
X
X
is properly contained in a connected
(
n
+
1
)
(n + 1)
-manifold, then
X
X
contains no
n
n
-dimensional umbrella (i.e. a set homeomorphic to the set
{
(
x
1
,
…
,
x
n
+
1
)
∈
E
n
+
1
:
x
1
2
+
⋯
+
x
n
+
1
2
≤
1
\{ ({x_1}, \ldots ,{x_{n + 1}}) \in {E^{n + 1}}:x_1^2 + \cdots + x_{n + 1}^2 \leq 1
and
x
n
+
1
≤
0
{x_{n + 1}} \leq 0
and either
x
1
=
⋯
=
x
n
=
0
{x_1} = \cdots = {x_n} = 0
or
x
n
+
1
=
0
}
{x_{n + 1}} = 0\}
). Combining this fact with an earlier result of the author we conclude that if
X
X
lies in
E
n
+
1
{E^{n + 1}}
and topologically contains
E
n
{E^n}
, then
X
X
is an
n
n
-manifold.