  We investigate spacetimes with their singular boundaries as noncommutative
spaces. Such a space is defined by a noncommutative algebra on a transformation
groupoid $\Gamma = E \times G$, where $E$ is the total space of the frame
bundle over spacetime with its singular boundary, and $G$ its structural group.
There is a bijective correspondence between unitary representations of the
groupoid $\Gamma $ and the systems of imprimitivity of the group $G$. This
allows us to apply the Mackey theorem, and deduce from it some information
concerning singular fibres of the groupoid. A subgroup $K$ of $G$, from which
-- according to the Mackey theorem -- the representation is induced to the
whole of $G$, can be regarded as measuring the "richness" of the singularity
structure.
