Let $X$ be an inner metric space with curvature bounded from below by $k$ in the sense of Toponogov. $\Sigma_p$ be the space of directions at point $p$. In the note by Plaut "Metric spaces of curvature bounded from below", the author mentioned thesis of Stephanie Gloor (1998, Zurich), which contains an example of an inner metric space with curvature $\ge k$ such that the space of directions at some point is not an inner metric space.

Does any one know this example?