  A limiting diagram for the Segre classification of the energy-momentum tensor
is obtained and discussed in connection with a Penrose specialization diagram
for the Segre types. A generalization of the coordinate-free approach to limits
of Paiva et al. to include non-vacuum space-times is made. Geroch's work on
limits of space-times is also extended. The same argument also justifies part
of the procedure for classification of a given spacetime using Cartan scalars.
