A homogeneous continuum that is non-Effros

Abstract:

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