Using a very geometric, intuitive construction, an example is given of a homogeneous, compact, connected Hausdorff space
(
X
,
T
)
(X,T)
that does not satisfy the conclusion of the Effros Theorem. In particular, there is a point
p
p
and a neighborhood
V
V
, of the identity in the group of self-homeomorphisms on
X
X
, with the compact-open topology such that
V
p
=
{
h
(
p
)
:
h
∈
V
}
{V_p} = \{ h(p):h \in V\}
is nowhere dense in
X
X
.