  Following a recent work in which it is shown that a spacetime admitting
Lie-group actions may be disjointly decomposed into a a closed subset with no
interior plus a dense finite union of open sets in each of which the character
and dimension of the group orbits as well as the Petrov type are constant, the
aim of this work is to include the Segre types of the Ricci tensor (and hence
of the Einstein tensor) into the decomposition. We also show how this type of
decomposition can be carried out for any type of property of the spacetime
depending on the existence of a continuous endomorphism.
